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 Approach To Optimization Problems With Equilibrium Constraints
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Author : Jiri Outrata
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07-31
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 1998-07-31 with Business & Economics categories.
This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.
Nonsmooth Optimization
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Author : Marko M. Mäkelä
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1992-01-01
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 1992-01-01 with Mathematics categories.
Introduces various methods for nonsmooth optimization and applies these methods to solve discretized nonsmooth optimal control problems of systems governed by boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR
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.
Just as in its 1st edition, 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. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. 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. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.
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.
Numerical Pde Constrained Optimization
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Author : Juan Carlos De los Reyes
language : en
Publisher: Springer
Release Date : 2015-02-06
Numerical Pde Constrained Optimization written by Juan Carlos De los Reyes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Mathematics categories.
This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.
Numerical Optimization
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Author : Jorge Nocedal
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-11
Numerical Optimization written by Jorge Nocedal 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 2006-12-11 with Mathematics categories.
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Nonsmooth Analysis And Control Theory
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Author : Francis H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-10
Nonsmooth Analysis And Control Theory written by Francis 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 2008-01-10 with Mathematics categories.
In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential equations, control theory, and, increasingly, in analysis. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercises. The book begins with an introductory chapter which gives the reader a sampling of what is to come while indicating at an early stage why the subject is of interest. The next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject leading to an efficient, natural, yet powerful body of theory. The last chapter, as its name implies, is a self-contained introduction to thetheory of control of ordinary differential equations. End-of-chapter problems also offer scope for deeper understanding. The authors have incorporated in the text a number of new results which clarify the relationships between the different schools of thought in the subject. Their goal is to make nonsmooth analysis accessible to a wider audience. In this spirit, the book is written so as to be used by anyone who has taken a course in functional analysis.
Methods Of Nonsmooth Optimization In Stochastic Programming
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Author : Wim Stefanus van Ackooij
language : en
Publisher: Springer Nature
Release Date : 2025-05-05
Methods Of Nonsmooth Optimization In Stochastic Programming written by Wim Stefanus van Ackooij and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Business & Economics categories.
This book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide—whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained.
Elliptic Problems In Nonsmooth Domains
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Author : Pierre Grisvard
language : en
Publisher: SIAM
Release Date : 2011-10-20
Elliptic Problems In Nonsmooth Domains written by Pierre Grisvard and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-20 with Mathematics categories.
Originally published: Boston: Pitman Advanced Pub. Program, 1985.