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Author: Zhi-Quan Luo
Publisher: Cambridge University Press
ISBN: 9780521572903
Category : Mathematics
Languages : en
Pages : 432
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Book Description
An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
Author: Zhi-Quan Luo
Publisher: Cambridge University Press
ISBN: 9780521572903
Category : Mathematics
Languages : en
Pages : 432
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Book Description
An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
Author: William E. Hart
Publisher: Springer Science & Business Media
ISBN: 146143226X
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This book provides a complete and comprehensive reference/guide to Pyomo (Python Optimization Modeling Objects) for both beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. The text illustrates the breadth of the modeling and analysis capabilities that are supported by the software and support of complex real-world applications. Pyomo is an open source software package for formulating and solving large-scale optimization and operations research problems. The text begins with a tutorial on simple linear and integer programming models. A detailed reference of Pyomo's modeling components is illustrated with extensive examples, including a discussion of how to load data from data sources like spreadsheets and databases. Chapters describing advanced modeling capabilities for nonlinear and stochastic optimization are also included. The Pyomo software provides familiar modeling features within Python, a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions. The software supports a different modeling approach than commercial AML (Algebraic Modeling Languages) tools, and is designed for flexibility, extensibility, portability, and maintainability but also maintains the central ideas in modern AMLs.
Author: Jiri Outrata
Publisher: Springer Science & Business Media
ISBN: 1475728255
Category : Mathematics
Languages : en
Pages : 281
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Book Description
In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.
Author: Zhi-Quan Luo
Publisher: Cambridge University Press
ISBN: 1316582612
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.
Author: Aram Arutyunov
Publisher: Springer Science & Business Media
ISBN: 9780792366553
Category : Mathematics
Languages : en
Pages : 318
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Book Description
This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Author: Hoai An Le Thi
Publisher: Springer
ISBN: 3030218031
Category : Technology & Engineering
Languages : en
Pages : 1164
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Book Description
This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
Author: S. K. Neogy
Publisher: World Scientific
ISBN: 9812813225
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications. Sample Chapter(s). Foreword (45 KB). Chapter 1: Mathematical Programming and its Applications in Finance (177 KB). Contents: Mathematical Programming and Its Applications in Finance (L C Thomas); Anti-Stalling Pivot Rule for Linear Programs with Totally Unimodular Coefficient Matrix (S N Kabadi & A P Punnen); A New Practically Efficient Interior Point Method for Convex Quadratic Programming (K G Murty); A General Framework for the Analysis of Sets of Constraints (R Caron & T Traynor), Tolerance-Based Algorithms for the Traveling Salesman Problem (D Ghosh et al.); On the Membership Problem of the Pedigree Polytope (T S Arthanari); Exact Algorithms for a One-Defective Vertex Colouring Problem (N Achuthan et al.); Complementarity Problem Involving a Vertical Block Matrix and Its Solution Using Neural Network Model (S K Neogy et al.); Fuzzy Twin Support Vector Machines for Pattern Classification (R Khemchandani et al.); An Overview of the Minimum Sum of Absolute Errors Regression (S C Narula & J F Wellington); Hedging Against the Market with No Short Selling (S A Clark & C Srinivasan); Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra Through Network Analysis (H Narayanan); Dynamic Optimal Control Policy in Price and Quality for High Technology Product (A K Bardhan & U Chanda); Forecasting for Supply Chain and Portfolio Management (K G Murty); Variational Analysis in Bilevel Programming (S Dempe et al.); Game Engineering (R J Aumann); Games of Connectivity (P Dubey & R Garg); A Robust Feedback Nash Equilibrium in a Climate Change Policy Game (M Hennlock); De Facto Delegation and Proposer Rules (H Imai & K Yonezaki); The Bargaining Set in Effectivity Function (D Razafimahatolotra); Dynamic Oligopoly as a Mixed Large Game OCo Toy Market (A Wiszniewska-Matyszkiel); On Some Classes of Balanced Games (R B Bapat); Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games (S Lahiri); Continuity, Manifolds, and Arrow''s Social Choice Problem (K Saukkonen); On a Mixture Class of Stochastic Games with Ordered Field Property (S K Neogy). Readership: Researchers, professionals and advanced students in mathematical programming, game theory, management sciences and computational mathematics.
Author: Christelle Guéret
Publisher: Twayne Publishers
ISBN: 9780954350307
Category : Linear programming
Languages : en
Pages : 349
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Book Description
Author: Paul R. Thie
Publisher: John Wiley & Sons
ISBN: 1118165454
Category : Mathematics
Languages : en
Pages : 476
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Book Description
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.
Author: Michael Patriksson
Publisher: Courier Dover Publications
ISBN: 0486802272
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.
