Holdings: Nondifferentiable optimization and polynomial problems

Nondifferentiable optimization and polynomial problems:

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Bibliographic Details
Main Author:	Shor, Naum Z. (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] Kluwer 1998
Series:	Nonconvex optimization and its applications 24
Subjects:	Mathematische programmering Optimaliseren Extremal problems (Mathematics) Mathematical optimization Nondifferentiable functions Nonlinear programming Polynomials Nichtdifferenzierbare Funktion Optimierung Polynom
Online Access:	Inhaltsverzeichnis
Physical Description:	XVII, 394 S.
ISBN:	0792349970

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MARC


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adam_text	NONDIFFERENTIABLE OPTIMIZATION AND POLYNOMIAL PROBLEMS BY NAUM Z. SHOR V.M. GLUSHKOV INSTITUTE OF CYBERNETICS, UKRAINIAN NATIONAL ACADEMY OF SCIENCES, KIEV KLUWER ACADEMIC PUBLISHERS BOSTON / DORDRECHT / LONDON CONTENTS PREFACE IX ELEMENTS OF CONVEX ANALYSIS, LINEAR ALGEBRA, AND GRAPH THEORY L 1.1 CONVEX SETS AND CONVEX FUNCTIONS 1 1.2 PROPERTIES OF SUBGRADIENT AND E-SUBGRADIENT SETS 8 1.3 KUHN-TUCKER THEOREM AND DUAL BOUNDS 19 1.4 NONSMOOTH PENALTY FUNCTIONS 22 1.5 POLYHEDRAL SETS, MATRICES AND QUADRATIC FUNCTIONS 25 1.6 ELEMENTS OF GRAPH THEORY 30 SUBGRADIENT AND E-SUBGRADIENT METHODS 35 2.1 THE SUBGRADIENT METHOD 37 2.2 FEJER-TYPE SUBGRADIENT METHODS 51 2.3 E-SUBGRADIENT AND BUNDLE METHODS 57 2.4 THE STOCHASTIC SUBGRADIENT METHOD 68 SUBGRADIENT-TYPE METHODS WITH SPACE DILATION 71 3.1 HEURISTICS OF METHODS WITH SPACE DILATION 71 3.2 THE SUBGRADIENT METHOD WITH SPACE DILATION IN THE DIREC- TION OF SUBGRADIENT 74 3.3 THE ELLIPSOID METHOD AND ITS GENERALIZATIONS 88 3.4 METHODS WITH SPACE DILATION IN DIRECTION OF THE DIFFERENCE OF TWO SUCCESSIVE SUBGRADIENTS IN TRANSFORMED SPACE 100 VI NONDIFFERENTIABLE OPTIMIZATION AND POLYNOMIAL PROBLEMS 4 ELEMENTS OF INFORMATION AND NUMERICAL COMPLEXITY OF POLYNOMIAL EXTREMAL PROBLEMS 113 4.1 INTRODUCTION TO THE COMPLEXITY THEORY OF OPTIMIZATION PROB- LEMS 113 4.2 POLYNOMIAL-TIME ALGORITHMS FOR LINEAR PROGRAMMING 118 4.3 INTERIOR POINT ALGORITHMS FOR LINEAR PROGRAMMING AND SPECIAL CONVEX PROGRAMMING PROBLEMS 121 4.4 REVIEW OF MAIN RESULTS ON COMPLEXITY THEORY OF POLYNOMIAL PROGRAMS 133 5 DECOMPOSITION METHODS BASED ON NONSMOOTH OPTIMIZATION 141 5.1 COORDINATE PROBLEMS ARISING IN DECOMPOSITION ON CONSTRAINTS 145 5.2 NONSMOOTH PROBLEMS LINKING WITH DECOMPOSITION ON VARI- ABLES 147 5.3 EXAMPLES OF SOLVING LARGE-SCALE PROBLEMS BY USING DECOM- POSITION SCHEMES IN COMBINATION WITH R- ALGORITHM ON HIGH- SPEED PARALLEL COMPUTERS 152 6 ALGORITHMS FOR CONSTRUCTING OPTIMAL ON VOLUME ELLIPSOIDS AND SEMIDEFINITE PROGRAMMING 169 6.1 INTRODUCTION 169 6.2 SIMPLE ALGORITHMS FOR CONSTRUCTING OPTIMAL ON VOLUME CIR- CUMSCRIBED ELLIPSOIDS 178 6.3 ALGORITHMS FOR CONSTRUCTING INSCRIBED ELLIPSOIDS OF MAXI- MUM VOLUME 187 6.4 INTERIOR POINT METHODS FOR DETERMINATION OF OPTIMAL CIRCUM- SCRIBED AND INSCRIBED ELLIPSOIDS 193 6.5 METHOD OF INSCRIBED ELLIPSOIDS FOR MINIMIZATION OF CONVEX FUNCTIONS ON POLYTOPES 196 6.6 SEMIDEFINITE PROGRAMMING PROBLEMS 200 6.7 SEMIDEFINITE PROGRAMMING MODELS IN AUTOMATIC CONTROL 210 6.8 NONCONVEX QUADRATIC PROGRAMS AND SEMIDEFINITE PROGRAM- MING V . 220 CONTENTS VII 7 THE ROLE OF ELLIPSOID METHOD FOR COMPLEXITY ANALYSIS OF COMBINATORIAL PROBLEMS 227 7.1 POLYNOMIAL EQUIVALENCE OF THE OPTIMIZATION AND SEPARATION PROBLEMS 227 7.2 JUSTIFICATION OF THE POLYNOMIAL-TIME SOLVABILITY OF SOME COM- BINATORIAL PROBLEMS 232 7.3 DUAL BOUNDS FOR MAXIMUM WEIGHTED STABLE SETS IN GRAPHS 239 7.4 POLYNOMIAL-TIME ALGORITHM FOR PERFECT GRAPHS 254 7.5 USING R-ALGORITHM FOR OBTAINING UPPER BOUNDS FOR THE MAX- IMUM WEIGHTED STABLE SET PROBLEMS 257 8 SEMIDEFINITE PROGRAMMING BOUNDS FOR EXTREMAL GRAPH PROBLEMS 265 8.1 THE MAXIMUM CUT PROBLEM 265 8.2 GRAPH PARTITIONING PROBLEMS 279 8.3 UPPER BOUNDS FOR THE SIZE OF FC-PARTITE INDUCED SUBGRAPHS OF GIVEN GRAPH AND THEIR APPLICATIONS TO COLOURING PROBLEMS 293 9 GLOBAL MINIMIZATION OF POLYNOMIAL FUNCTIONS AND 17-TH HILBERT PROBLEM 299 9.1 THE PROBLEM OF REPRESENTATION OF NONNEGATIVE POLYNOMIALS AS SUM OF SQUARES OF POLYNOMIALS 299 9.2 CONSTRUCTING OF QUADRATIC PROBLEM WITH SUPERFLUOUS CON- STRAINTS FOR GLOBAL MINIMIZATION OF ONE-DIMENSIONAL POLYNO- MIALS 308 9.3 NECESSARY AND SUFFICIENT CONDITIONS FOR DUAL QUADRATIC BOUND TO BE EXACT. MULTIDIMENSIONAL CASE 320 9.4 INSTANCES OF FINDING GLOBAL MINIMUM OF POLYNOMIAL FUNCTIONS USING R-ALGORITHM 330 REFERENCES 335
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indexdate	2024-07-09T18:26:21Z
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isbn	0792349970
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owner	DE-703 DE-11
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physical	XVII, 394 S.
publishDate	1998
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publisher	Kluwer
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series	Nonconvex optimization and its applications
series2	Nonconvex optimization and its applications
spelling	Shor, Naum Z. Verfasser aut Nondifferentiable optimization and polynomial problems by Naum Z. Shor Boston [u.a.] Kluwer 1998 XVII, 394 S. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 24 Mathematische programmering gtt Optimaliseren gtt Extremal problems (Mathematics) Mathematical optimization Nondifferentiable functions Nonlinear programming Polynomials Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Optimierung (DE-588)4043664-0 s Polynom (DE-588)4046711-9 s Nichtdifferenzierbare Funktion (DE-588)4326748-8 s DE-604 Nonconvex optimization and its applications 24 (DE-604)BV010085908 24 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008387634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Shor, Naum Z. Nondifferentiable optimization and polynomial problems Nonconvex optimization and its applications Mathematische programmering gtt Optimaliseren gtt Extremal problems (Mathematics) Mathematical optimization Nondifferentiable functions Nonlinear programming Polynomials Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Optimierung (DE-588)4043664-0 gnd Polynom (DE-588)4046711-9 gnd
subject_GND	(DE-588)4326748-8 (DE-588)4043664-0 (DE-588)4046711-9
title	Nondifferentiable optimization and polynomial problems
title_auth	Nondifferentiable optimization and polynomial problems
title_exact_search	Nondifferentiable optimization and polynomial problems
title_full	Nondifferentiable optimization and polynomial problems by Naum Z. Shor
title_fullStr	Nondifferentiable optimization and polynomial problems by Naum Z. Shor
title_full_unstemmed	Nondifferentiable optimization and polynomial problems by Naum Z. Shor
title_short	Nondifferentiable optimization and polynomial problems
title_sort	nondifferentiable optimization and polynomial problems
topic	Mathematische programmering gtt Optimaliseren gtt Extremal problems (Mathematics) Mathematical optimization Nondifferentiable functions Nonlinear programming Polynomials Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Optimierung (DE-588)4043664-0 gnd Polynom (DE-588)4046711-9 gnd
topic_facet	Mathematische programmering Optimaliseren Extremal problems (Mathematics) Mathematical optimization Nondifferentiable functions Nonlinear programming Polynomials Nichtdifferenzierbare Funktion Optimierung Polynom
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008387634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010085908
work_keys_str_mv	AT shornaumz nondifferentiableoptimizationandpolynomialproblems

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