Numerical Nonsmooth Optimization
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Numerical Nonsmooth Optimization
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Author : Adil M. Bagirov
language : en
Publisher: Springer Nature
Release Date : 2020-02-28
Numerical Nonsmooth Optimization written by Adil M. Bagirov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Business & Economics categories.
Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.
Nonsmooth Optimization
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Author : Marko M. Mäkelä
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1992-05
Nonsmooth Optimization written by Marko M. Mäkelä and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05 with Mathematics categories.
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.
Methods Of Dynamic And Nonsmooth Optimization
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Author : Frank H. Clarke
language : en
Publisher: SIAM
Release Date : 1989-01-01
Methods Of Dynamic And Nonsmooth Optimization written by Frank H. Clarke and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
Presents the elements of a unified approach to optimization based on 'nonsmooth analysis', a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.
Introduction To Nonsmooth Optimization
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Author : Adil Bagirov
language : en
Publisher: Springer
Release Date : 2014-08-12
Introduction To Nonsmooth Optimization written by Adil Bagirov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Business & Economics categories.
This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints
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Author : Jiri Outrata
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints written by Jiri Outrata and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Numerical Optimization
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Author : Joseph-Frédéric Bonnans
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Numerical Optimization written by Joseph-Frédéric Bonnans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.
Nonsmooth Optimization And Related Topics
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Author : F.H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Nonsmooth Optimization And Related Topics written by F.H. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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
Recent Advances In Nonsmooth Optimization
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Author : Ding-zhu Du
language : en
Publisher: World Scientific
Release Date : 1995-09-20
Recent Advances In Nonsmooth Optimization written by Ding-zhu Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-20 with Mathematics categories.
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.
Numerical Methods For Structured Problems In Nonsmooth Optimization
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Author : Robert Spencer Womersley
language : en
Publisher:
Release Date : 1981
Numerical Methods For Structured Problems In Nonsmooth Optimization written by Robert Spencer Womersley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Calculus of variations categories.
Nonsmooth Equations In Optimization
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Author : Diethard Klatte
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-17
Nonsmooth Equations In Optimization written by Diethard Klatte and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-17 with Mathematics categories.
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.