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Titlebook: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints; Theory, Applications Jiři Outrata,Michal Kočvara,Jochem Zowe Book

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书目名称Nonsmooth Approach to Optimization Problems with Equilibrium Constraints
副标题Theory, Applications
编辑Jiři Outrata,Michal Kočvara,Jochem Zowe
视频videohttp://file.papertrans.cn/668/667876/667876.mp4
丛书名称Nonconvex Optimization and Its Applications
图书封面Titlebook: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints; Theory, Applications Jiři Outrata,Michal Kočvara,Jochem Zowe Book
描述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 n
出版日期Book 1998
关键词Newton‘s method; Optimality Conditions; algorithm; algorithms; calculus; continuum mechanics; mechanics; mo
版次1
doihttps://doi.org/10.1007/978-1-4757-2825-5
isbn_softcover978-1-4419-4804-5
isbn_ebook978-1-4757-2825-5Series ISSN 1571-568X
issn_series 1571-568X
copyrightSpringer-Verlag US 1998
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Stability of Solutions to Perturbed Generalized Equationsn the Lipschitz behaviour of these solutions. In this chapter we present the part of this theory relevant to our later applications. We assume that the generalized equations from the previous chapter are now subjected to perturbations and we analyse the local behaviour of the associated solution maps . Basically, we follow Robinson’s work.
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Membrane with ObstacleWe start the application part of the book with a classic example of an elliptic variational inequality—an elastic membrane with an obstacle. First, we describe the state problem and then, in the subsequent sections, three shape optimization problems of graded complexity.
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Economic ApplicationsCentral to many aspects of economic analysis (and even political theory) is the concept of equilibrium. Similarly as in mechanics, formal characterizations of this concept typically come as complementarity problems or variational inequalities.
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Nonconvex Optimization and Its Applicationshttp://image.papertrans.cn/n/image/667876.jpg
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https://doi.org/10.1007/978-1-4757-2825-5Newton‘s method; Optimality Conditions; algorithm; algorithms; calculus; continuum mechanics; mechanics; mo
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