A Nonsmooth Approach To Optimization Problems With Equilibrium Constraints
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| Author | : Jiri Outrata |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475728255 |
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 |
| Total Pages | : 432 |
| Release | : 1996-11-13 |
| Genre | : Mathematics |
| ISBN | : 9780521572903 |
An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
| Author | : Altannar Chinchuluun |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 351 |
| Release | : 2012-11-28 |
| Genre | : Mathematics |
| ISBN | : 1461451310 |
Optimization, simulation and control play an increasingly important role in science and industry. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. This volume brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. The book is composed of invited contributions by experts from around the world who work to develop and apply new optimization, simulation and control techniques either at a theoretical level or in practice. Some key topics presented include: equilibrium problems, multi-objective optimization, variational inequalities, stochastic processes, numerical analysis, optimization in signal processing, and various other interdisciplinary applications. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization, simulation and control can be applied.
| Author | : Vivek Laha |
| Publisher | : Springer Nature |
| Total Pages | : 441 |
| Release | : 2021-07-27 |
| Genre | : Mathematics |
| ISBN | : 9811618194 |
This book includes selected papers presented at the Indo-French Seminar on Optimization, Variational Analysis and Applications (IFSOVAA-2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 2–4 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, interval-valued optimization, sequential quadratic programming, bound-constrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems.
| Author | : Anurag Jayswal |
| Publisher | : CRC Press |
| Total Pages | : 309 |
| Release | : 2022-09-13 |
| Genre | : Technology & Engineering |
| ISBN | : 1000648982 |
The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.
| Author | : Ashkan Nikeghbali |
| Publisher | : Springer Nature |
| Total Pages | : 417 |
| Release | : 2022-08-04 |
| Genre | : Mathematics |
| ISBN | : 3031008324 |
This volume presents extensive research devoted to a broad spectrum of mathematics with emphasis on interdisciplinary aspects of Optimization and Probability. Chapters also emphasize applications to Data Science, a timely field with a high impact in our modern society. The discussion presents modern, state-of-the-art, research results and advances in areas including non-convex optimization, decentralized distributed convex optimization, topics on surrogate-based reduced dimension global optimization in process systems engineering, the projection of a point onto a convex set, optimal sampling for learning sparse approximations in high dimensions, the split feasibility problem, higher order embeddings, codifferentials and quasidifferentials of the expectation of nonsmooth random integrands, adjoint circuit chains associated with a random walk, analysis of the trade-off between sample size and precision in truncated ordinary least squares, spatial deep learning, efficient location-based tracking for IoT devices using compressive sensing and machine learning techniques, and nonsmooth mathematical programs with vanishing constraints in Banach spaces. The book is a valuable source for graduate students as well as researchers working on Optimization, Probability and their various interconnections with a variety of other areas. Chapter 12 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
| Author | : Michael C. Ferris |
| Publisher | : SIAM |
| Total Pages | : 494 |
| Release | : 1997-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898713916 |
After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.
| Author | : Ronald Hoppe |
| Publisher | : Springer |
| Total Pages | : 422 |
| Release | : 2014-09-11 |
| Genre | : Computers |
| ISBN | : 3319080253 |
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).
| Author | : Vladimir Shikhman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 200 |
| Release | : 2011-11-18 |
| Genre | : Mathematics |
| ISBN | : 1461418976 |
This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory.
| Author | : Fausto Pedro García Márquez |
| Publisher | : Springer |
| Total Pages | : 274 |
| Release | : 2016-11-15 |
| Genre | : Computers |
| ISBN | : 3319454986 |
This book focuses on the analytic principles of business practice and big data. Specifically, it provides an interface between the main disciplines of engineering/technology and the organizational and administrative aspects of management, serving as a complement to books in other disciplines such as economics, finance, marketing and risk analysis. The contributors present their areas of expertise, together with essential case studies that illustrate the successful application of engineering management theories in real-life examples.
