A conical approach to linear programming: scalar and vector optimization problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Gordon and Breach Science Publ.
1997
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 290 S. graph. Darst. |
| ISBN: | 9056990314 |
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| adam_text | A CONICAL APPROACH TO LINEAR PROGRAMMING SCALAR AND VECTOR OPTIMIZATION
PROBLEMS PAOLO D ALESSANDRO DEPARTMENT OF MATHEMATICS THIRD UNIVERSITY
OFROME, ITALY GORDON AND BREACH SCIENCE PUBLISHERS AUSTRALIA * CANADA *
CHINA FRANCE * GERMANY * INDIA * JAPAN LUXEMBOURG * MALAYSIA * THE
NETHERLANDS * RUSSIA * SINGAPORE SWITZERLAND * THAILAND * UNITED KINGDOM
CONTENTS PREFACE XI INTRODUCTION XIII PART I: GENERAL THEORY 1 A GENERAL
CONICAL APPROACH TO OPTIMIZATION 3 1.1 FUNDAMENTAL CONICAL FEASIBILITY
AND OPTIMALITY CONDITIONS 6 1.2 CONICAL APPROACH TO INEQUALITY
CONSTRAINED OPTIMIZATION 12 2 ESSENTIAL BACKGROUND 16 2.1 LINEAR AND
AFFINE SUB SPACES, CONVEX SETS 17 2.2 CONVEX CONES AND LINEALITY SPACES
18 2.3 EXTENSIONS AND ELEMENTARY COMPUTATIONS 19 2.4 HILBERT SPACES,
OPERATORS AND DECOMPOSITION OF CONES 22 2.5 GENERALIZATION OF THE
ORTHOGONAL PROTECTION 26 2.6 CONVEX SUBSETS OF R N , EXTREME POINTS AND
FACES 27 2.7 NORMAL CONES AND POLARITY 29 2.8 POLYHEDRA AND POLYHEDRAL
CONES 31 3 LINEAR OPTIMIZATION PROBLEMS IN EUCLIDEAN SPACES 37 3.1
LINEAR PROGRAMMING PROBLEM FORMULATION 38 3.2 OTHER FORMULATIONS OF THE
LP PROBLEM AND A SPECIAL LP PROBLEM 40 3.3 LINEAR MULTICRITERIA
OPTIMIZATION PROBLEMS 43 3.4 ROBUST LINEAR OPTIMIZATION PROBLEMS 44 3.5
PARAMETERS VARIATIONS 45 4 CONICAL OPTIMALITY CONDITIONS FOR LINEAR
PROGRAMMING 48 4.1 PARAMETERIZED FEASIBILITY FORMULATION OF THE LP
PROBLEM 48 VU RIUE * CONTENTS 4.2 PRIMAL FEASIBILITY AND OPTIMALITY
CONDITIONS 50 4.3 DUAL OPTIMALITY CONDITIONS 54 5 DUAL CONICAL
ALGORITHMS 59 5.1 FEASIBILITY 59 5.2 FEASIBILITY AND PARAMETERS
VARIATIONS 60 5.3 OPTIMALITY 67 5.4 OPTIMALITY AND PARAMETERS VARIATIONS
71 5.5 A CLUE TO THE EXISTENCE OF AN EQUIVALENT RELAXATION 72 6 RELATIVE
POSITION OF A SUBSPACE AND THE NON-NEGATIVE ORTHANT 74 6.1 STRICTLY
TANGENT, WEAKLY TANGENT AND INTERNAL SUBSPACES 75 6.2 ORTHOGONAL
COMPLEMENTS AND THE NON-NEGATIVE ORTHANT 81 6.3 FIRST CONSEQUENCES FOR
LF AND LP PROBLEMS 85 6.4 GORDAN AND STIENKE DUALITY THEOREMS 87 6.5
DUAL PAIRS AND THE CONICAL APPROACH 88 7 DETERMINING THE MAXIMAL FACE OF
THE NON-NEGATIVE ORTHANT, WHOSE RELATIVE INTERIOR IS MET BY A SUBSPACE
90 7.1 METHODS FOR THE IDENTIFICATION OF M AND FOR FINDING A VECTOR IN F
N M 1 91 7.2 ON THE DEVELOPMENT OF ALGORITHMS FOR COMPUTING M AND FOR
FINDING A VECTOR IN F N M 1 93 8 THEORYOFTHE STRICTLY TANGENT RELAXATION
94 8.1 MAINRESULTS 97 8.2 INTERVAL LINEAR PROGRAM (CONTINUED FROM
SECTIONS 3.2 AND 6.1) 103 9 THE CONE INTERSECTION OF THE NON-NEGATIVE
ORTHANT AND A LINEAR SUBSPACE 107 9.1 THE EXTREME RAYS OF THE CONE
INTERSECTION OF A SUBSPACE AND THE NON-NEGATIVE ORTHANT 109 9.2 THE
EXTREME RAYS OF THE CONE F X N P 111 9.3 BASIC ALGORITHM FOR THE
COMPUTATION OF EXTREME RAYS 114 9.4 THE COMBINATORIAL EXPLOSION AND AN
UPPER BOUND FOR THE NUMBER OF GENERATORS 118 9.5 THE GENERATORS, THE
STRICTLY TANGENT RELAXATION, AND REFINED BOUNDS FOR THE NUMBER OF
GENERATORS 120 CONTENTS IX 9.6 RELAXATIONS AND RESTRICTIONS 123 10 THE
CONE SUM OF THE NON-NEGATIVE ORTHANT AND A LINEAR SUBSPACE 126 10.1 THE
DECOMPOSITION OF THE CONE SUM OF THE NON-NEGATIVE ORTHANT AND A SUBSPACE
127 10.2 CONSEQUENCES FOR LF AND LP PROBLEMS 134 11 THE PRIMAL CONICAL
ALGORITHM 136 11.1 SETTING FOR THE PRIMAL CONICAL ALGORITHM 136 11.2
PRIMAL CONICAL ALGORITHM 137 11.3 CONVERGENCE 140 11.4 STRICT FINITE
CONVERGENCE 145 12 LINEAR VECTOR OPTIMIZATION 152 12.1 EXTENSION OF THE
CONICAL APPROACH TO VECTOR OPTIMIZATION 154 12.2 ASSESSING FEASIBILITY
AND BOUNDEDNESS 156 12.3 VECTOR OPTIMALITY CONDITION 157 12.4 ALGORITHM
FOR THE SOLUTION OF THE VLP PROBLEM 158 13 ROBUST LINEAR OPTIMIZATION
161 13.1 PROBLEM DEFINITION 162 13.2 DUAL CONICAL SOLUTION OF THE ROBUST
OPTIMIZATION PROBLEM 162 PART II: FURTHER ADVANCED RESULTS 14 ADVANCED
DUAL ALGORITHM 169 14.1 TECHNIQUES FOR ACCELERATING THE COMPUTATION OF
GENERATORS 170 14.2 MINIMUM DISTANCE OF TWO CLOSED CONVEX SETS 177 15
FURTHER RESULTS ON PARAMETERS VARIATIONS 179 15.1 ADDING OR VARYING
CONSTRAINTS AND FUNCTIONALS 179 15.2 RECURSIVE ALGORITHM ON THE
COLUMNSOFG* 182 15.3 ADDING A VARIABLE 184 PART III: IMPLEMENTATIONS AND
NUMERICAL RESULTS 16 IMPLEMENTATION OFTHE DUAL ALGORITHM 189 16.1
CONSTANTS, TYPES AND GLOBAL VARIABLES 190 16.2 REVIEW OF SERVICE
PROCEDURES 197 X CONTENTS 16.3 THE MAIN AND INITIALIZATION PROCEDURES
202 16.4 COMPUTATION OF GENERATORS 204 16.5 PROCEDURES FOR COMPUTING THE
SOLUTION 217 17 IMPLEMENTATION OF THE PRIMAL ALGORITHM 227 17.1
CONSTANTS, TYPES AND GLOBAL VARIABLES 228 17.2 THE MAIN 228 17.3
IMPLEMENTATION OF THE ALGORITHM 229 18 NUMERICAL RESULTS 232 18.1 AN
EXAMPLE SOLVED BY MEANS OF BOTH THE DUAL AND THE PRIMAL ALGORITHM 232
18.2 A STATISTICAL EXPERIMENT 237 18.3 CONCLUSIONS AND RESEARCH
ORIENTATIONS 240 PART IV: MODULA/2 LISTINGS APPENDIX 1: MODULA-2 LISTING
OF DUALCON 245 APPENDIX 2: MODULA-2 LISTING OF PRIMACON 270 REFERENCES
286 INDEX 289
|
| any_adam_object | 1 |
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| dewey-full | 519.7/2 |
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| dewey-raw | 519.7/2 |
| dewey-search | 519.7/2 |
| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | D'Alessandro, Paolo Verfasser aut A conical approach to linear programming scalar and vector optimization problems Paolo d'Alessandro Amsterdam Gordon and Breach Science Publ. 1997 XXII, 290 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007910045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | D'Alessandro, Paolo A conical approach to linear programming scalar and vector optimization problems Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | A conical approach to linear programming scalar and vector optimization problems |
| title_auth | A conical approach to linear programming scalar and vector optimization problems |
| title_exact_search | A conical approach to linear programming scalar and vector optimization problems |
| title_full | A conical approach to linear programming scalar and vector optimization problems Paolo d'Alessandro |
| title_fullStr | A conical approach to linear programming scalar and vector optimization problems Paolo d'Alessandro |
| title_full_unstemmed | A conical approach to linear programming scalar and vector optimization problems Paolo d'Alessandro |
| title_short | A conical approach to linear programming |
| title_sort | a conical approach to linear programming scalar and vector optimization problems |
| title_sub | scalar and vector optimization problems |
| topic | Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Linear programming Mathematical optimization Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007910045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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