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.
Nonsmooth Optimization and Related Topics
Nonsmooth Optimization and Related Topics - 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 Optimization and Related Topics write by F.H. Clarke. This book was released on 2013-11-11. Nonsmooth Optimization and Related Topics available in PDF, EPUB and Kindle. This volume contains the edited texts of the lect. nres presented at the International School of Mathematics devoted to Nonsmonth Optimization, held from . June 20 to July I, 1988. The site for the meeting was the "Ettore ~Iajorana" Centre for Sci entific Culture in Erice, Sicily. In the tradition of these meetings the main purpose was to give the state-of-the-art of an important and growing field of mathematics, and to stimulate interactions between finite-dimensional and infinite-dimensional op timization. The School was attended by approximately 80 people from 23 countries; in particular it was possible to have some distinguished lecturers from the SO\·iet Union, whose research institutions are here gratt-fnlly acknowledged. Besides the lectures, several seminars were delivered; a special s·~ssion was devoted to numerical computing aspects. The result was a broad exposure. gi ·. ring a deep knowledge of the present research tendencies in the field. We wish to express our appreciation to all the participants. Special mention 5hould be made of the Ettorc ;. . Iajorana Centre in Erice, which helped provide a stimulating and rewarding experience, and of its staff which was fundamental for the success of the meeting. j\, loreover, WP want to extend uur deep appreci
Nonsmooth Equations in Optimization
Nonsmooth Equations in Optimization - 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 Equations in Optimization write by Diethard Klatte. This book was released on 2005-12-17. Nonsmooth Equations in Optimization available in PDF, EPUB and Kindle. Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control
Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control - 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 Optimization: Analysis And Algorithms With Applications To Optimal Control write by Marko M Makela. This book was released on 1992-05-07. Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control available in PDF, EPUB and Kindle. This book is a self-contained elementary study for nonsmooth analysis and optimization, and their use in solution of nonsmooth optimal control problems. The first part of the book is concerned with nonsmooth differential calculus containing necessary tools for nonsmooth optimization. The second part is devoted to the methods of nonsmooth optimization and their development. A proximal bundle method for nonsmooth nonconvex optimization subject to nonsmooth constraints is constructed. In the last part nonsmooth optimization is applied to problems arising from optimal control of systems covered by partial differential equations. Several practical problems, like process control and optimal shape design problems are considered.
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.
