Nondifferentiable Optimization: Motivations and Applications
Author: Vladimir Fedorovich Demʹi︠a︡nov
Publisher:
Published: 1984
Total Pages: 346
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Vladimir Fedorovich Demʹi︠a︡nov
Publisher:
Published: 1984
Total Pages: 346
ISBN-13:
DOWNLOAD EBOOKAuthor: Vladimir F. Demyanov
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 355
ISBN-13: 3662126036
DOWNLOAD EBOOKThe 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 in organiz ing this meeting.
Author: Vladimir Fedorovich Demʹi︠a︡nov
Publisher: Springer
Published: 1985
Total Pages: 368
ISBN-13:
DOWNLOAD EBOOKAuthor: Vladimir Fedorovich Demyanov
Publisher:
Published: 1985
Total Pages: 349
ISBN-13:
DOWNLOAD EBOOKAuthor: Cees Withagen
Publisher:
Published: 1985
Total Pages: 172
ISBN-13:
DOWNLOAD EBOOKAuthor: Vladimir Fedorovich Demʹi͡anov
Publisher:
Published: 1985
Total Pages: 349
ISBN-13: 9780387159799
DOWNLOAD EBOOKAuthor: Vladimir F. Demyanov
Publisher: Springer
Published: 1985-10-01
Total Pages: 355
ISBN-13: 9783540159797
DOWNLOAD EBOOKThe 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 in organiz ing this meeting.
Author: V.F. Dem'yanov
Publisher: Springer
Published: 1985-12-12
Total Pages: 452
ISBN-13: 9780387909516
DOWNLOAD EBOOKOf 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].
Author: Vladimir Fedorovich Dem'yanov
Publisher:
Published: 1997
Total Pages: 452
ISBN-13: 9785855011081
DOWNLOAD EBOOKAuthor: V.F. Dem'yanov
Publisher: Springer
Published: 2012-08-14
Total Pages: 0
ISBN-13: 9781461382683
DOWNLOAD EBOOKOf 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].