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| bi-level optimization example: Metaheuristics for Bi-level Optimization El-Ghazali Talbi, 2013-04-09 This book provides a complete background on metaheuristics to solve complex bi-level optimization problems (continuous/discrete, mono-objective/multi-objective) in a diverse range of application domains. Readers learn to solve large scale bi-level optimization problems by efficiently combining metaheuristics with complementary metaheuristics and mathematical programming approaches. Numerous real-world examples of problems demonstrate how metaheuristics are applied in such fields as networks, logistics and transportation, engineering design, finance and security. |
| bi-level optimization example: Practical Bilevel Optimization Jonathan F. Bard, 1998-12-31 The focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology. What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field. Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists. |
| bi-level optimization example: Bilevel Programming Problems Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés, Nataliya Kalashnykova, 2015-01-28 This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained. |
| bi-level optimization example: Foundations of Bilevel Programming Stephan Dempe, 2005-12-19 Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful. |
| bi-level optimization example: Multilevel Optimization: Algorithms and Applications A. Migdalas, Panos M. Pardalos, Peter Värbrand, 2013-12-01 Researchers working with nonlinear programming often claim the word is non linear indicating that real applications require nonlinear modeling. The same is true for other areas such as multi-objective programming (there are always several goals in a real application), stochastic programming (all data is uncer tain and therefore stochastic models should be used), and so forth. In this spirit we claim: The word is multilevel. In many decision processes there is a hierarchy of decision makers, and decisions are made at different levels in this hierarchy. One way to handle such hierar chies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierar chy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of opti mization problems which must be solved in a predetermined sequence. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level). |
| bi-level optimization example: Knowledge-Based and Intelligent Information and Engineering Systems, Part I Andreas Koenig, Andreas Dengel, Knut Hinkelmann, Koichi Kise, Robert J. Howlett, Lakhmi C. Jain, 2011-09-06 The four-volume set LNAI 6881-LNAI 6884 constitutes the refereed proceedings of the 15th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2011, held in Kaiserslautern, Germany, in September 2011. Part 1: The total of 244 high-quality papers presented were carefully reviewed and selected from numerous submissions. The 61 papers of Part 1 are organized in topical sections on artificial neural networks, connectionists systems and evolutionary computation, machine learning and classical AI, agent, multi-agentsystems, knowledge based and expert systems, intelligent vision, image processing and signal processing, knowledge management, ontologies, and data mining. |
| bi-level optimization example: Computational Combinatorial Optimization Michael Jünger, Denis Naddef, 2001-11-21 This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality. |
| bi-level optimization example: State of the Art in Global Optimization Christodoulos A. Floudas, Panos M. Pardalos, 2013-12-01 Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on State of the Art in Global Optimization: Computational Methods and Applications held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications. |
| bi-level optimization example: Hydrogen Supply Chain Catherine Azzaro-Pantel, 2018-08-18 Design, Deployment and Operation of a Hydrogen Supply Chain introduces current energy system and the challenges that may hinder the large-scale adoption of hydrogen as an energy carrier. It covers the different aspects of a methodological framework for designing a HSC, including production, storage, transportation and infrastructure. Each technology's advantages and drawbacks are evaluated, including their technology readiness level (TRL). The multiple applications of hydrogen for energy are presented, including use in fuel cells, combustion engines, as an alternative to natural gas and power to gas. Through analysis and forecasting, the authors explore deployment scenarios, considering the dynamic aspect of HSCs. In addition, the book proposes methods and tools that can be selected for a multi-criteria optimal design, including performance drivers and economic, environmental and societal metrics. Due to its systems-based approach, this book is ideal for engineering professionals, researchers and graduate students in the field of energy systems, energy supply and management, process systems and even policymakers. - Explores the key drivers of hydrogen supply chain design and performance evaluation, including production and storage facilities, transportation, information, sourcing, pricing and sustainability - Presents multi-criteria tools for the optimization of hydrogen supply chains and their integration in the overall energy system - Examines the available technology, their strengths and weaknesses, and their technology readiness levels (TRL), to draw future perspectives of hydrogen markets and propose deployment scenarios - Includes international case studies of hydrogen supply chains at various scales |
| bi-level optimization example: Multi-Level Decision Making Guangquan Zhang, Jie Lu, Ya Gao, 2015-02-07 This monograph presents new developments in multi-level decision-making theory, technique and method in both modeling and solution issues. It especially presents how a decision support system can support managers in reaching a solution to a multi-level decision problem in practice. This monograph combines decision theories, methods, algorithms and applications effectively. It discusses in detail the models and solution algorithms of each issue of bi-level and tri-level decision-making, such as multi-leaders, multi-followers, multi-objectives, rule-set-based, and fuzzy parameters. Potential readers include organizational managers and practicing professionals, who can use the methods and software provided to solve their real decision problems; PhD students and researchers in the areas of bi-level and multi-level decision-making and decision support systems; students at an advanced undergraduate, master’s level in information systems, business administration, or the application of computer science. |
| bi-level optimization example: Bilevel Optimization Stephan Dempe, Alain Zemkoho, 2020-11-23 2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization. |
| bi-level optimization example: Derivative-Free and Blackbox Optimization Charles Audet, Warren Hare, 2017-12-02 This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix. |
| bi-level optimization example: Convex Optimization Stephen P. Boyd, Lieven Vandenberghe, 2004-03-08 Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics. |
| bi-level optimization example: Mathematical Programs with Equilibrium Constraints Zhi-Quan Luo, Jong-Shi Pang, Daniel Ralph, 1996-11-13 An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints. |
| bi-level optimization example: An Introduction to Linear Programming and Game Theory Paul R. Thie, Gerard E. Keough, 2011-09-15 Praise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science. |
| bi-level optimization example: Applications of Optimization with Xpress-MP Christelle Guéret, Christian Prins, Marc Sevaux, 2002 |
| bi-level optimization example: Ant Colony Optimization Marco Dorigo, Thomas Stutzle, 2004-06-04 An overview of the rapidly growing field of ant colony optimization that describes theoretical findings, the major algorithms, and current applications. The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioinformatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms. |
| bi-level optimization example: Algorithms for Optimization Mykel J. Kochenderfer, Tim A. Wheeler, 2019-03-12 A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals. |
| bi-level optimization example: Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers Stephen Boyd, Neal Parikh, Eric Chu, 2011 Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. |
| bi-level optimization example: High-level Synthesis Michael Fingeroff, 2010 Are you an RTL or system designer that is currently using, moving, or planning to move to an HLS design environment? Finally, a comprehensive guide for designing hardware using C++ is here. Michael Fingeroff's High-Level Synthesis Blue Book presents the most effective C++ synthesis coding style for achieving high quality RTL. Master a totally new design methodology for coding increasingly complex designs! This book provides a step-by-step approach to using C++ as a hardware design language, including an introduction to the basics of HLS using concepts familiar to RTL designers. Each chapter provides easy-to-understand C++ examples, along with hardware and timing diagrams where appropriate. The book progresses from simple concepts such as sequential logic design to more complicated topics such as memory architecture and hierarchical sub-system design. Later chapters bring together many of the earlier HLS design concepts through their application in simplified design examples. These examples illustrate the fundamental principles behind C++ hardware design, which will translate to much larger designs. Although this book focuses primarily on C and C++ to present the basics of C++ synthesis, all of the concepts are equally applicable to SystemC when describing the core algorithmic part of a design. On completion of this book, readers should be well on their way to becoming experts in high-level synthesis. |
| bi-level optimization example: A Gentle Introduction to Optimization B. Guenin, J. Könemann, L. Tunçel, 2014-07-31 Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material. |
| bi-level optimization example: Engineering Design Optimization Joaquim R. R. A. Martins, Andrew Ning, 2021-11-18 Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments. |
| bi-level optimization example: Spot Pricing of Electricity Fred C. Schweppe, Michael C. Caramanis, Richard D. Tabors, Roger E. Bohn, 2013-03-07 There is a need for fundamental changes in the ways society views electric energy. Electric energy must be treated as a commodity which can be bought, sold, and traded, taking into account its time-and space-varying values and costs. This book presents a complete framework for the establishment of such an energy marketplace. The framework is based on the use of spot prices. In general terms: o An hourly spot price (in dollars per kilowatt hour) reflects the operating and capital costs of generating, transmitting and distributing electric energy. It varies each hour and from place to place. o The spot price based energy marketplace involves a variety of utility-customer transactions (ranging from hourly varying prices to long-term, multiple-year contracts), all of which are based in a consistent manner on hourly spot prices. These transactions may include customers selling to, as well as buying from, the utility. The basic theory and practical implementation issues associated with a spot price based energy marketplace have been developed and discussed through a number of different reports, theses, and papers. Each addresses only a part of the total picture, and often with a somewhat different notation and terminology (which has evolved in parallel with our growing experience). This book was xvii xviii Preface written to serve as a single, integrated sourcebook on the theory and imple mentation of a spot price based energy marketplace. |
| bi-level optimization example: Convex Analysis and Nonlinear Optimization Jonathan Borwein, Adrian S. Lewis, 2010-05-05 Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs. |
| bi-level optimization example: Iterative Methods in Combinatorial Optimization Lap Chi Lau, R. Ravi, Mohit Singh, 2011-04-18 With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms. |
| bi-level optimization example: Aimms Optimization Modeling Johannes Bisschop, 2006 The AIMMS Optimization Modeling book provides not only an introduction to modeling but also a suite of worked examples. It is aimed at users who are new to modeling and those who have limited modeling experience. Both the basic concepts of optimization modeling and more advanced modeling techniques are discussed. The Optimization Modeling book is AIMMS version independent. |
| bi-level optimization example: Robust Optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski, 2009-08-10 Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject. |
| bi-level optimization example: Numerical Optimization Jorge Nocedal, Stephen Wright, 2006-12-11 Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization. |
| bi-level optimization example: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models F. Giannessi, A. Maugeri, Panos M. Pardalos, 2006-04-11 The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained. |
| bi-level optimization example: Practical Optimization Philip E. Gill, Walter Murray, Margaret H. Wright, 2019-12-16 In the intervening years since this book was published in 1981, the field of optimization has been exceptionally lively. This fertility has involved not only progress in theory, but also faster numerical algorithms and extensions into unexpected or previously unknown areas such as semidefinite programming. Despite these changes, many of the important principles and much of the intuition can be found in this Classics version of Practical Optimization. This book provides model algorithms and pseudocode, useful tools for users who prefer to write their own code as well as for those who want to understand externally provided code. It presents algorithms in a step-by-step format, revealing the overall structure of the underlying procedures and thereby allowing a high-level perspective on the fundamental differences. And it contains a wealth of techniques and strategies that are well suited for optimization in the twenty-first century, and particularly in the now-flourishing fields of data science, big data, and machine learning. Practical Optimization is appropriate for advanced undergraduates, graduate students, and researchers interested in methods for solving optimization problems. |
| bi-level optimization example: A First Course in Optimization Charles Byrne, 2014-08-11 Give Your Students the Proper Groundwork for Future Studies in OptimizationA First Course in Optimization is designed for a one-semester course in optimization taken by advanced undergraduate and beginning graduate students in the mathematical sciences and engineering. It teaches students the basics of continuous optimization and helps them better |
| bi-level optimization example: Lectures on Modern Convex Optimization Aharon Ben-Tal, Arkadi Nemirovski, 2001-01-01 Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications. |
| bi-level optimization example: Multi-level Mixed-Integer Optimization Styliani Avraamidou, Efstratios Pistikopoulos, 2022-06-06 This book provides the fundamental underlying mathematical theory, numerical algorithms and effi cient computational tools for the solution of multi-level mixedinteger optimization problems. It can enable a vast array of decision makers and engineers (e.g. process engineers, bioengineers, chemical and civil engineers, and economists) to model, formulate and solve hierarchical decision making problems. The book gives detailed insights on multi-level optimization by comprehensive explanations, step-by-step numerical examples and case studies, plots, and diagrams. |
| bi-level optimization example: Evolutionary Multiobjective Optimization Ajith Abraham, Robert Goldberg, 2005-09-05 Evolutionary Multi-Objective Optimization is an expanding field of research. This book brings a collection of papers with some of the most recent advances in this field. The topic and content is currently very fashionable and has immense potential for practical applications and includes contributions from leading researchers in the field. Assembled in a compelling and well-organised fashion, Evolutionary Computation Based Multi-Criteria Optimization will prove beneficial for both academic and industrial scientists and engineers engaged in research and development and application of evolutionary algorithm based MCO. Packed with must-find information, this book is the first to comprehensively and clearly address the issue of evolutionary computation based MCO, and is an essential read for any researcher or practitioner of the technique. |
| bi-level optimization example: Variational Analysis R. Tyrrell Rockafellar, Roger J.-B. Wets, 2009-06-26 From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands. |
| bi-level optimization example: Optimization and Decision Support Design Guide: Using IBM ILOG Optimization Decision Manager Axel Buecker, Yana Ageeva, Veronique Blanchard, Dr. Jeremy Bloom, Dr. Mehmet F. Candas, Joao Chaves, Guang Feng, Abhishek Raman, Dr. Hans Schlenker, IBM Redbooks, 2012-10-10 Today many organizations face challenges when developing a realistic plan or schedule that provides the best possible balance between customer service and revenue goals. Optimization technology has long been used to find the best solutions to complex planning and scheduling problems. A decision-support environment that enables the flexible exploration of all the trade-offs and sensitivities needs to provide the following capabilities: Flexibility to develop and compare realistic planning and scheduling scenarios Quality sensitivity analysis and explanations Collaborative planning and scenario sharing Decision recommendations This IBM® Redbooks® publication introduces you to the IBM ILOG® Optimization Decision Manager (ODM) Enterprise. This decision-support application provides the capabilities you need to take full advantage of optimization technology. Applications built with IBM ILOG ODM Enterprise can help users create, compare, and understand planning or scheduling scenarios. They can also adjust any of the model inputs or goals, and fully understanding the binding constraints, trade-offs, sensitivities, and business options. This book enables business analysts, architects, and administrators to design and use their own operational decision management solution. |
| bi-level optimization example: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. |
| bi-level optimization example: Optimization by Vector Space Methods David G. Luenberger, 1997-01-23 Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book. |
| bi-level optimization example: Multi-Objective Optimization using Evolutionary Algorithms Kalyanmoy Deb, 2001-07-05 Optimierung mit mehreren Zielen, evolutionäre Algorithmen: Dieses Buch wendet sich vorrangig an Einsteiger, denn es werden kaum Vorkenntnisse vorausgesetzt. Geboten werden alle notwendigen Grundlagen, um die Theorie auf Probleme der Ingenieurtechnik, der Vorhersage und der Planung anzuwenden. Der Autor gibt auch einen Ausblick auf Forschungsaufgaben der Zukunft. |
| bi-level optimization example: Optimization Methods in Finance Gerard Cornuejols, Reha Tütüncü, 2006-12-21 Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses. |
什么是BI，当前国内外BI的现状，BI的应用状况？ - 知乎
什么是BI？ BI（BusinessIntelligence）即商业智能，它是一套完整的解决方案，用来将企业中现有的数据进行有效的整合，快速准确的提供报表并提出决策依据，帮助企业做出明智的业务经营 …
关于Power BI的下载和安装，你想知道的都在这里了 - 知乎
Apr 5, 2025 · 我的图书《Power BI商业数据分析》已出版，帮你从0到1，轻松入门: 学习和使用PowerBI ，离不开PowerBI Desktop，每个人开始学习的第一步就是先安装软件。 关于PowerBI …
BI工具的意义有多大？到底是IT人用还是业务人用？ - 知乎
3、自助分析. bi自助分析模式是从传统“it主导的报表模式”向“业务主导的自助服务分析模式”重大转变，这一转变的价值在企业中也得到了验证，满足企业不同人群对数据查询、分析和探索的需 …
有哪些开源的BI工具？ - 知乎
现在市场上开源 BI 产品比较多，各个产品的侧重点不同，有的以报表为主、有的以可视化为主、有的以查询分析为主。这里我们选取了一些主流的开源 BI 产品，从产品功能、可视化能力、 …
Win10自带输入法无法输入中文怎么解决？ - 知乎
KB4516058 这个更新会引起在任务管理器里多1个Microsoft IME 的 高CPU进程，该进程CPU使用过高除了会导致电脑卡顿，有时会使win10输入法无法切换 （简单说就是打不了中文了）
FineBI和PowerBI对比？ - 知乎
Power BI的创建和设计旨在构建MS Excel的功能，将其升级到下一个级别，进一步扩展其可操作性以解锁新的用例，覆盖更多的平台并接触到云。 作为微软的产品，Power BI与微软工具带中 …
知乎 - 有问题，就会有答案
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
有没有免费的BI软件？ - 知乎
那到底有 bi 需求又注重成本的客户应该怎么选 bi 呢？ 如果注重成本的话，商业 BI 工具一般也就不太符合，商用软件价格较高，而且现在用户的需求比较灵活，往往需要页面端的定制开发，这 …
BI工程师需要掌握那些技术？ - 知乎
大概说下一个成熟的商业智能bi工程师的技术能力，可以沿着这些点来规划自己的职业生涯： 商业智能bi的技术能力. 通常 5 年以上的商业智能bi行业从业经验，经历过若干个不同类型的项 …
如何将PowerBI作品发布到web？ - 知乎
在 Power BI 服务中，选择要共享的报表，以在画布上显示。 然后，在菜单中选择“文件”>“发布到 Web”。 随即将出现一个对话框，说明你将收到一个嵌入代码，允许将报表包含在网站或电子 …
什么是BI，当前国内外BI的现状，BI的应用状况？ - 知乎
什么是BI？ BI（BusinessIntelligence）即商业智能，它是一套完整的解决方案，用来将企业中现有的数据进行有效的整合，快速准确的提供报表并提出决策依据，帮助企业做出明智的业务经营决策。
关于Power BI的下载和安装，你想知道的都在这里了 - 知乎
Apr 5, 2025 · 我的图书《Power BI商业数据分析》已出版，帮你从0到1，轻松入门: 学习和使用PowerBI ，离不开PowerBI Desktop，每个人开始学习的第一步就是先安装软件。 关于PowerBI软件下载和安 …
BI工具的意义有多大？到底是IT人用还是业务人用？ - 知乎
3、自助分析. bi自助分析模式是从传统“it主导的报表模式”向“业务主导的自助服务分析模式”重大转变，这一转变的价值在企业中也得到了验证，满足企业不同人群对数据查询、分析和探索的需求，真正 …
有哪些开源的BI工具？ - 知乎
现在市场上开源 BI 产品比较多，各个产品的侧重点不同，有的以报表为主、有的以可视化为主、有的以查询分析为主。这里我们选取了一些主流的开源 BI 产品，从产品功能、可视化能力、数据源支持以 …
Win10自带输入法无法输入中文怎么解决？ - 知乎
KB4516058 这个更新会引起在任务管理器里多1个Microsoft IME 的 高CPU进程，该进程CPU使用过高除了会导致电脑卡顿，有时会使win10输入法无法切换 （简单说就是打不了中文了）
FineBI和PowerBI对比？ - 知乎
Power BI的创建和设计旨在构建MS Excel的功能，将其升级到下一个级别，进一步扩展其可操作性以解锁新的用例，覆盖更多的平台并接触到云。 作为微软的产品，Power BI与微软工具带中的其他软件 …
知乎 - 有问题，就会有答案
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区 …
有没有免费的BI软件？ - 知乎
那到底有 bi 需求又注重成本的客户应该怎么选 bi 呢？ 如果注重成本的话，商业 BI 工具一般也就不太符合，商用软件价格较高，而且现在用户的需求比较灵活，往往需要页面端的定制开发，这个商用软件 …
BI工程师需要掌握那些技术？ - 知乎
大概说下一个成熟的商业智能bi工程师的技术能力，可以沿着这些点来规划自己的职业生涯： 商业智能bi的技术能力. 通常 5 年以上的商业智能bi行业从业经验，经历过若干个不同类型的项目，周期从几 …
如何将PowerBI作品发布到web？ - 知乎
在 Power BI 服务中，选择要共享的报表，以在画布上显示。 然后，在菜单中选择“文件”>“发布到 Web”。 随即将出现一个对话框，说明你将收到一个嵌入代码，允许将报表包含在网站或电子邮件中。
