Nondifferentiable Optimization

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Methods Of Descent For Nondifferentiable Optimization

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Author : Krzysztof C. Kiwiel
language : en
Publisher: Springer
Release Date : 2006-11-14

Methods Of Descent For Nondifferentiable Optimization written by Krzysztof C. Kiwiel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.

Nondifferentiable Optimization And Polynomial Problems

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Author : N.Z. Shor
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-31

Nondifferentiable Optimization And Polynomial Problems written by N.Z. Shor 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 1998-03-31 with Mathematics categories.

Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.

Nondifferentiable Optimization Motivations And Applications

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Author : Vladimir F. Demyanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Nondifferentiable Optimization Motivations And Applications written by Vladimir F. Demyanov 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 Business & Economics categories.

The International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria, has been involved in research on nondifferentiable optimization since 1976. IIASA-based East-West cooperation in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimi zation has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition, and to review recent developments in this field, IIASA held a Workshop on Nondifferentiable Optimization in Sopron (Hungary) in September 1964. The aims of the Workshop were: 1. To discuss the state-of-the-art of nondifferentiable optimization (NDO), its origins and motivation; 2. To compare-various algorithms; 3. To evaluate existing mathematical approaches, their applications and potential; 4. To extend and deepen industrial and other applications of NDO. The following topics were considered in separate sessions: General motivation for research in NDO: nondifferentiability in applied problems, nondifferentiable mathematical models. Numerical methods for solving nondifferentiable optimization problems, numerical experiments, comparisons and software. Nondifferentiable analysis: various generalizations of the concept of subdifferen tials. Industrial and other applications. This volume contains selected papers presented at the Workshop. It is divided into four sections, based on the above topics: I. Concepts in Nonsmooth Analysis II. Multicriteria Optimization and Control Theory III. Algorithms and Optimization Methods IV. Stochastic Programming and Applications We would like to thank the International Institute for Applied Systems Analysis, particularly Prof. V. Kaftanov and Prof. A.B. Kurzhanski, for their support inorganiz ing this meeting.

Nondifferentiable Optimization

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Author : Vladimir Fedorovich Demʹi︠a︡nov
language : en
Publisher:
Release Date : 1985

Nondifferentiable Optimization written by Vladimir Fedorovich Demʹi︠a︡nov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

Modern Nonconvex Nondifferentiable Optimization

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Author : Ying Cui
language : en
Publisher: SIAM
Release Date : 2021-12-02

Modern Nonconvex Nondifferentiable Optimization written by Ying Cui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Mathematics categories.

Starting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in statistical estimation, operations research, machine learning, and decision making. A comprehensive and rigorous treatment of this emergent mathematical topic is urgently needed in today’s complex world of big data and machine learning. This book takes a thorough approach to the subject and includes examples and exercises to enrich the main themes, making it suitable for classroom instruction. Modern Nonconvex Nondifferentiable Optimization is intended for applied and computational mathematicians, optimizers, operations researchers, statisticians, computer scientists, engineers, economists, and machine learners. It could be used in advanced courses on optimization/operations research and nonconvex and nonsmooth optimization.

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".

Progress In Nondifferentiable Optimization

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Author : E. A. Nurminski
language : en
Publisher:
Release Date : 1982

Progress In Nondifferentiable Optimization written by E. A. Nurminski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Algorithms categories.

Nondifferentiable Optimization

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Author : Philip Wolfe
language : en
Publisher:
Release Date : 1975

Nondifferentiable Optimization written by Philip Wolfe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Functions of real variables categories.

Nondifferentiable Optimization

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Author : V.F. Dem'yanov
language : en
Publisher: Springer
Release Date : 2012-08-14

Nondifferentiable Optimization written by V.F. Dem'yanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-14 with Science categories.

Of recent coinage, the term "nondifferentiable optimization" (NDO) covers a spectrum of problems related to finding extremal values of nondifferentiable functions. Problems of minimizing nonsmooth functions arise in engineering applications as well as in mathematics proper. The Chebyshev approximation problem is an ample illustration of this. Without loss of generality, we shall consider only minimization problems. Among nonsmooth minimization problems, minimax problems and convex problems have been studied extensively ([31], [36], [57], [110], [120]). Interest in NDO has been constantly growing in recent years (monographs: [30], [81], [127] and articles and papers: [14], [20], [87]-[89], [98], [130], [135], [140]-[142], [152], [153], [160], all dealing with various aspects of non smooth optimization). For solving an arbitrary minimization problem, it is neces sary to: 1. Study properties of the objective function, in particular, its differentiability and directional differentiability. 2. Establish necessary (and, if possible, sufficient) condi tions for a global or local minimum. 3. Find the direction of descent (steepest or, simply, feasible--in appropriate sense). 4. Construct methods of successive approximation. In this book, the minimization problems for nonsmooth func tions of a finite number of variables are considered. Of fun damental importance are necessary conditions for an extremum (for example, [24], [45], [57], [73], [74], [103], [159], [163], [167], [168].

Nodifferentiable Optimization

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Author :
language : en
Publisher:
Release Date : 1975

Nodifferentiable Optimization written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.