Author : Yun Lu
Publisher :
Page : pages
File Size : 23,57 MB
Release : 2020
Category :
ISBN :
Study of Theory and Algorithms for Nonsmooth Variational Inequalities
Yun Lu
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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
F. Giannessi
Author : F. Giannessi
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 22,60 MB
Release : 2006-04-11
Category : Mathematics
ISBN : 0306480263
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.
Regularity Concepts in Nonsmooth Analysis
Messaoud Bounkhel
Author : Messaoud Bounkhel
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 46,81 MB
Release : 2011-11-12
Category : Mathematics
ISBN : 1461410193
The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature.
Recent Advances in Nonsmooth Optimization
Dingzhu Du
Author : Dingzhu Du
Publisher : World Scientific
Page : 488 pages
File Size : 46,88 MB
Release : 1995
Category : Mathematics
ISBN : 9789810222659
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.
Nonsmooth Optimization: Analysis And Algorithms With Applications To Optimal Control
Marko M Makela
Author : Marko M Makela
Publisher : World Scientific
Page : 268 pages
File Size : 30,76 MB
Release : 1992-05-07
Category : Mathematics
ISBN : 9814522414
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.
Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization
Qamrul Hasan Ansari
Author : Qamrul Hasan Ansari
Publisher : CRC Press
Page : 294 pages
File Size : 33,1 MB
Release : 2013-07-18
Category : Business & Economics
ISBN : 1439868212
Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.The first part of the book focuses on generalized convexity and generalized
Nonlinear Programming and Variational Inequality Problems
Michael Patriksson
Author : Michael Patriksson
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 20,81 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 147572991X
Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.
Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization
Qamrul Hasan Ansari
Author : Qamrul Hasan Ansari
Publisher : CRC Press
Page : 298 pages
File Size : 43,49 MB
Release : 2013-07-18
Category : Business & Economics
ISBN : 1439868204
Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction. The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.
Mathematical Theory of Hemivariational Inequalities and Applications
Zdzistaw Naniewicz
Author : Zdzistaw Naniewicz
Publisher : CRC Press
Page : 291 pages
File Size : 30,55 MB
Release : 2021-07-28
Category : Mathematics
ISBN : 1000445054
Gives a complete and rigorous presentation of the mathematical study of the expressions - hemivariational inequalities - arising in problems that involve nonconvex, nonsmooth energy functions. A theory of the existence of solutions for inequality problems involving monconvexity and nonsmoothness is established.
Equilibrium Problems and Variational Models
P. Daniele
Author : P. Daniele
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 19,2 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461302390
The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.