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.
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.
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 Optimization In Honor Of The 60th Birthday Of Adil M Bagirov
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Author : Napsu Karmitsa
language : en
Publisher: MDPI
Release Date : 2020-12-18
Nonsmooth Optimization In Honor Of The 60th Birthday Of Adil M Bagirov written by Napsu Karmitsa and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Science categories.
The aim of this book was to collect the most recent methods developed for NSO and its practical applications. The book contains seven papers: The first is the foreword by the Guest Editors giving a brief review of NSO and its real-life applications and acknowledging the outstanding contributions of Professor Adil Bagirov to both the theoretical and practical aspects of NSO. The second paper introduces a new and very efficient algorithm for solving uncertain unit-commitment (UC) problems. The third paper proposes a new nonsmooth version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems. In the fourth paper, the abs-linear representation of piecewise linear functions is extended to yield simultaneously their DC decomposition as well as the pair of generalized gradients. The fifth paper presents the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and nonsmooth optimization problems in many practical applications. In the sixth paper, a problem concerning the scheduling of nuclear waste disposal is modeled as a nonsmooth multiobjective mixed-integer nonlinear optimization problem, and a novel method using the two-slope parameterized achievement scalarizing functions is introduced. Finally, the last paper considers binary classification of a multiple instance learning problem and formulates the learning problem as a nonconvex nonsmooth unconstrained optimization problem with a DC objective function.
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.
Nonsmooth Optimization And Its Applications
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Author : Seyedehsomayeh Hosseini
language : en
Publisher: Birkhäuser
Release Date : 2019-04-16
Nonsmooth Optimization And Its Applications written by Seyedehsomayeh Hosseini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Mathematics categories.
Since nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem’s scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed a rich and sophisticated set of mathematical tools at the intersection of theory and practice. This volume of ISNM is an outcome of the workshop "Nonsmooth Optimization and its Applications," which was held from May 15 to 19, 2017 at the Hausdorff Center for Mathematics, University of Bonn. The six research articles gathered here focus on recent results that highlight different aspects of nonsmooth and variational analysis, optimization methods, their convergence theory and applications.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Nonsmooth Mechanics Of Solids
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Author : Jaroslav Haslinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-03
Nonsmooth Mechanics Of Solids written by Jaroslav Haslinger 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 2007-08-03 with Computers categories.
Mechanics have played an important role in mathematics, from infinitesimal calculus, calculus of variations, partial differential equations and numerical methods (finite elements). Originally, mechanics treated smooth objects. Technological progress has evoked the necessity to model and solve more complicated problems, like unilateral contact and friction, plasticity, delamination and adhesion, advanced materials, etc. The new tools include convex analysis, differential calculus for convex functions, and subgradients of convex functions and extensions for nonconvex problems. Nonsmooth mechanics is a relatively complex field, and requires a good knowledge of mechanics and a good background in some parts of modern mathematics. The present volume of lecture notes follows a very successful advanced school, with the aim to cover as much as possible all these aspects. Therefore the contributions cover mechanical aspects as well as the mathematical and numerical treatment.
An Introduction To Numerical Methods Of Nonsmooth Optimization And Some Applications In Structural Optimization
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Author : Wolfgang Achtziger
language : en
Publisher:
Release Date : 1998
An Introduction To Numerical Methods Of Nonsmooth Optimization And Some Applications In Structural Optimization written by Wolfgang Achtziger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
An Introduction To Numerical Methods Of Nonsmooth Optimization And Some Applications In Structural Optimization
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Author : Wolfgang Achtziger
language : de
Publisher:
Release Date : 1998
An Introduction To Numerical Methods Of Nonsmooth Optimization And Some Applications In Structural Optimization written by Wolfgang Achtziger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.