The Theory Of Subgradients And Its Applications To Problems Of Optimization
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The Theory Of Subgradients And Its Applications To Problems Of Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher:
Release Date : 1978
The Theory Of Subgradients And Its Applications To Problems Of Optimization written by R. Tyrrell Rockafellar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Convex functions categories.
The Theory Of Subgradients And Its Applications To Problems Of Optimization
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Author : R. Tyrrell Rockafellar
language : en
Publisher:
Release Date : 1981
The Theory Of Subgradients And Its Applications To Problems Of Optimization written by R. Tyrrell Rockafellar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
The Theory Of Subgradients And Its Applications To Problems Of Optimization
DOWNLOAD eBooks
Author : R. Tyrrell Rockafellar
language : en
Publisher:
Release Date : 1978
The Theory Of Subgradients And Its Applications To Problems Of Optimization written by R. Tyrrell Rockafellar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
The Theory Of Subgradients And Its Applications To Problem Of Optimization Convex And Nonconvex Functions
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Author : Ralph Tyrrell Rockafellar
language : en
Publisher:
Release Date : 1981
The Theory Of Subgradients And Its Applications To Problem Of Optimization Convex And Nonconvex Functions written by Ralph Tyrrell Rockafellar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
The Projected Subgradient Algorithm In Convex Optimization
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2020-11-25
The Projected Subgradient Algorithm In Convex Optimization written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.
Optimization On Solution Sets Of Common Fixed Point Problems
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Author : Alexander J. Zaslavski
language : en
Publisher:
Release Date : 2021
Optimization On Solution Sets Of Common Fixed Point Problems written by Alexander J. Zaslavski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors. The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient. All results presented are new. Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.
Nonlinear Functional Analysis And Its Applications
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Author : E. Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Nonlinear Functional Analysis And Its Applications written by E. Zeidler 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 2013-12-11 with Science categories.
As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.
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.
Variational Analysis
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Author : R. Tyrrell Rockafellar
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-26
Variational Analysis written by R. Tyrrell Rockafellar 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 2009-06-26 with Mathematics categories.
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Nonlinear Optimization
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Author : H. A. Eiselt
language : en
Publisher: Springer Nature
Release Date : 2019-11-09
Nonlinear Optimization written by H. A. Eiselt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-09 with Mathematics categories.
This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.