Holdings: Optimization on low rank nonconvex structures

Optimization on low rank nonconvex structures:

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Bibliographic Details
Main Authors:	Konno, Hiroshi (Author), Thach, Phan Thien (Author), Tuy, Hoang (Author)
Format:	Book
Language:	English
Published:	Dordrecht [u.a.] Kluwer 1997
Series:	Nonconvex optimization and its applications 15
Subjects:	Mathematical optimization Globale Optimierung Nichtkonvexe Optimierung
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 457 S. graph. Darst.
ISBN:	0792343085

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MARC


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adam_text	OPTIMIZATION ON LOW RANK NONCONVEX STRUCTURES BY HIROSHI KONNO TOKYO INSTITUTE OF TECHNOLOGY TOKYO, JAPAN PHAN THIEN THACH HANOI INSTITUTE OF MATHEMATICS HANOI, VIETNAM AND HOANG TUY HANOI INSTITUTE OF MATHEMATICS HANOI, VIETNAM KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE IX PART I FOUNDATIONS 1 1 SCOPE OF GLOBAL OPTIMIZATION 3 1.1 MODELS AND NATURE OF THE PROBLEM 4 1.2 MATHEMATICAL STRUCTURE 10 1.3 HIERARCHY OF GLOBAL OPTIMIZATION PROBLEMS 13 1.4 TRANSCENDING STATIONARITY AS THE CORE OF GLOBAL OPTIMIZA- TION 15 1.5 PROBLEMS WITH SPECIAL STRUCTURES 18 2 QUASI-CONVEXITY 23 2.1 QUASI-CONVEX FUNCTIONS 24 2.2 QUASI-CONJUGACY 30 2.3 QUASI-BICONJUGATE 39 2.4 QUASI-SUBDIFFERENTIAL 43 3 D.C. FUNCTIONS AND D.C. SETS 47 3.1 SOME TYPICAL EXAMPLES 47 3.2 GENERAL PROPERTIES OF D.C. FUNCTIONS 50 3.3 HOW TO RECOGNIZE D.C. FUNCTIONS 52 3.4 EFFECTIVE D.C. REPRESENTATION 56 3.5 D.C. SETS 67 3.6 GLOBAL OPTIMALITY CRITERION 72 VI OPTIMIZATION ON LOW RANK NONCONVEX STRUCTURES 4 DUALITY 77 4.1 QUASI-CONVEX MINIMIZATION OVER-A CONVEX SET 78 4.2 MAXIMIZATION OVER A CONVEX SET AND MINIMIZATION OVER THE COMPLEMENT OF A CONVEX SET 85 4.3 D.C. OPTIMIZATION 93 5 LOW-RANK NONCONVEX STRUCTURES 95 5.1 NONCONVEXITY RANK 96 5.2 NONCONVEXITY INDEX 100 5.3 WEAKLY CONVEX FUNCTIONS 108 5.4 D.C. REPRESENTATION BY A NUCLEUS 113 6 GLOBAL SEARCH METHODS AND BASIC D.C. OPTIMIZATION ALGORITHMS 119 6.1 OUTER APPROXIMATION 119 6.2 SUCCESSIVE PARTITION 130 6.3 DUALIZATION 155 PART II METHODS AND ALGORITHMS 167 7 PARAMETRIC APPROACHES IN GLOBAL OPTIMIZATION 169 7.1 MINIMIZATION OF A GENERALIZED LINEAR MULTIPLICATIVE FUNC- TION AND A SUM OF TWO LINEAR FRACTIONAL FUNCTIONS 170 7.2 RANK TWO AND RANK THREE BILINEAR PROGRAMMING PROBLEMS 177 7.3 AVERAGE PERFORMANCE OF PARAMETRIC ALGORITHMS 184 7.4 MINIMIZATION OF LOW-RANK CONCAVE FUNCTIONS 191 8 MULTIPLICATIVE PROGRAMMING PROBLEMS 203 8.1 CONVEX MULTIPLICATIVE PROGRAMMING PROBLEMS 204 8.2 MINIMIZATION OF A PRODUCT OF SEVERAL CONVEX FUNCTIONS 213 8.3 OTHER PROBLEMS RELATED TO MULTIPLICATIVE FUNCTIONS 220 9 MONOTONIC PROBLEMS 229 9.1 QUASICONCAVE MONOTONIC FUNCTIONS 230 9.2 BASIC STRUCTURAL PROPERTIES 234 9.3 LINEARLY CONSTRAINED PROBLEMS 240 CONTENTS VII 9.4 SOLUTION-METHODS FOR MONOTONIC PROBLEMS 244 9.5 DECOMPOSITION BY POLYHEDRAL ANNEXATION 247 9.6 DECOMPOSITION BY PROJECTION 252 9.7 PROBLEMS WITH MONOTONIC CONSTRAINTS 258 9.8 CASES OF POLYNOMIAL SOLVABILITY: NETWORK CONSTRAINTS 264 10 DECOMPOSITION METHODS BY PRICES 273 10.1 GENERALIZED DANTZIG-WOLFE S DECOMPOSITION METHOD 274 10.2 GENERALIZED BENDERS PARTITIONING METHOD 283 10.3 ALTERNATIVE VARIANT 291 11 DYNAMIC PROGRAMMING ALGORITHMS IN GLOBAL OPTIMIZATION 297 11.1 MULTI-ECHELON PRODUCTION AND INVENTORY PROBLEM 298 11.2 LOT-SIZING PROBLEMS WITH GENERALIZED CONCAVE COST FUNC- TIONS 303 11.3 DISCRETE-VARIABLE MULTI-STAGE PROBLEMS 310 PART III SELECTED APPLICATIONS 323 12 LOW RANK NONCONVEX QUADRATIC PROGRAMMING 325 12.1 CONCAVE QUADRATIC PROGRAMMING PROBLEMS AND BILINEAR PROGRAMMING PROBLEMS 326 12.2 LOW RANK CONCAVE QUADRATIC PROGRAMMING PROBLEMS 331 12.3 LOW RANK BILINEAR PROGRAMMING PROBLEMS 343 12.4 GENERAL LOW RANK NONCONVEX QUADRATIC PROGRAMMING PROB- LEMS 349 13 CONTINUOUS LOCATION 353 13.1 UNCONSTRAINED LOCATION PROBLEMS 354 13.2 SOLVING UNCONSTRAINED LOCATION PROBLEMS 362 13.3 CONSTRAINED LOCATION PROBLEMS 367 13.4 SOLVING GENERAL CONSTRAINED LOCATION PROBLEMS 371 VLLL OPTIMIZATION ON LOW RANK NONCONVEX STRUCTURES 14 DESIGN CENTERING AND RELATED GEOMETRIC PROBLEMS 375 14.1 .DESIGN CENTERING 375 14.2 RELATED GEOMETRIC PROBLEMS 389 15 MULTIOBJECTIVE AND BILEVEL PROGRAMMING 397 15.1 OPTIMIZATION OVER THE EFFICIENT SET 398 15.2 BILEVEL LINEAR PROGRAMMING 408 15.3 RELATIONSHIP BETWEEN MONOTONIC, MULTIOBJECTIVE AND BILEVEL PROGRAMMING 423 REFERENCES 427 INDEX 455
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author	Konno, Hiroshi Thach, Phan Thien Tuy, Hoang
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isbn	0792343085
language	English
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physical	XI, 457 S. graph. Darst.
publishDate	1997
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publishDateSort	1997
publisher	Kluwer
record_format	marc
series	Nonconvex optimization and its applications
series2	Nonconvex optimization and its applications
spelling	Konno, Hiroshi Verfasser aut Optimization on low rank nonconvex structures by Hiroshi Konno, Phan Thien Thach and Hoang Tuy Dordrecht [u.a.] Kluwer 1997 XI, 457 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 15 Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s Nichtkonvexe Optimierung (DE-588)4309215-9 s DE-604 Thach, Phan Thien Verfasser aut Tuy, Hoang Verfasser aut Nonconvex optimization and its applications 15 (DE-604)BV010085908 15 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007792675&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Konno, Hiroshi Thach, Phan Thien Tuy, Hoang Optimization on low rank nonconvex structures Nonconvex optimization and its applications Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd
subject_GND	(DE-588)4140067-7 (DE-588)4309215-9
title	Optimization on low rank nonconvex structures
title_auth	Optimization on low rank nonconvex structures
title_exact_search	Optimization on low rank nonconvex structures
title_full	Optimization on low rank nonconvex structures by Hiroshi Konno, Phan Thien Thach and Hoang Tuy
title_fullStr	Optimization on low rank nonconvex structures by Hiroshi Konno, Phan Thien Thach and Hoang Tuy
title_full_unstemmed	Optimization on low rank nonconvex structures by Hiroshi Konno, Phan Thien Thach and Hoang Tuy
title_short	Optimization on low rank nonconvex structures
title_sort	optimization on low rank nonconvex structures
topic	Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd
topic_facet	Mathematical optimization Globale Optimierung Nichtkonvexe Optimierung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007792675&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010085908
work_keys_str_mv	AT konnohiroshi optimizationonlowranknonconvexstructures AT thachphanthien optimizationonlowranknonconvexstructures AT tuyhoang optimizationonlowranknonconvexstructures

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