Nonsmooth Approach to Optimization Problems with Equilibrium Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonsmooth Approach to Optimization Problems with Equilibrium Constraints write by Jiri Outrata. This book was released on 2013-06-29. Nonsmooth Approach to Optimization Problems with Equilibrium Constraints available in PDF, EPUB and Kindle. 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.
A Nonsmooth Approach to Optimization Problems with Equilibrium Constraints
A Nonsmooth Approach to Optimization Problems with Equilibrium Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Nonsmooth Approach to Optimization Problems with Equilibrium Constraints write by Michal Kočvara. This book was released on 1996. A Nonsmooth Approach to Optimization Problems with Equilibrium Constraints available in PDF, EPUB and Kindle.
Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models write by F. Giannessi. This book was released on 2006-04-11. Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models available in PDF, EPUB and Kindle. 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.
Mathematical Programs with Equilibrium Constraints
Mathematical Programs with Equilibrium Constraints - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Programs with Equilibrium Constraints write by Zhi-Quan Luo. This book was released on 1996-11-13. Mathematical Programs with Equilibrium Constraints available in PDF, EPUB and Kindle. An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC
Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC write by Didier Aussel. This book was released on 2018-04-03. Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC available in PDF, EPUB and Kindle. The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.
