High performance optimization:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Applied optimization
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 473 S. graph. Darst. |
| ISBN: | 0792360133 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | HIGH PERFORMANCE OPTIMIZATION EDITED BY HANS FRENK ERASMUS UNIVERSITY,
ROTTERDAM, THE NETHERLANDS KEES ROOS DELFT UNIVERSITY OF TECHNOLOGY, THE
NETHERLANDS TAMAES TERLAKY DELFT UNIVERSITY OF TECHNOLOGY, THE
NETHERLANDS AND SHUZHONG ZHANG ERASMUS UNIVERSITY, ROTTERDAM, THE
NETHERLANDS FF KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
CONTENTS LIST OF FIGURES XI LIST OF TABLES XIII PREFACE XV CONTRIBUTING
AUTHORS XVII PART I THEORY AND ALGORITHMS OF SEMIDEFINITE PROGRAMMING
JOS F. STURM 1 INTRODUCTION 3 1. APPLICATIONS 4 2. NOTATION 7 2.1 SETS
AND LINEAR SPACES 7 2.2 MATRICES AND VECTORIZATION 7 2.3 NORM AND
DISTANCE 10 2.4 BIG O AND SMALL O 11 3. CONIC FORM 12 3.1 SEMIDEFINITE
PROGRAMMING 12 3.2 CONIC CONVEX PROGRAMMING 13 4. ORGANIZATION 14
APPENDIX: HERMITIAN MATRICES 17 1. EIGENVALUE DECOMPOSITION 17 2.
CHOLESKY DECOMPOSITION 18 3. SIMILARITY 18 4. SCHUR COMPLEMENT 19 2
DUALITY 21 1. TERMINOLOGY AND PRELIMINARIES 22 2. BASIC PROPERTIES OF
CONVEX CONES 26 V VI HIGH PERFORMANCE OPTIMIZATION TECHNIQUES 3.
CHARACTERIZATION OF STRONG FEASIBILITY 29 4. FARKAS-TYPE LEMMAS 33 5.
STRONG DUALITY 36 6. REGULARIZATION 43 7. REGULARIZATION OF SEMIDEFINITE
PROGRAMS 50 8. INEXACT DUAL SOLUTIONS 56 9. DISCUSSION 60 3
POLYNOMIALITY OF 61 PATH-FOLLOWING METHODS 1. PRIMAL-DUAL
TRANSFORMATIONS 61 2. THE NEWTON DIRECTION 66 3. NEIGHBORHOODS OF THE
CENTRAL PATH 70 4. TECHNICAL RESULTS 71 5. FOUR PATH-FOLLOWING
ALGORITHMS 76 5.1 THE SHORT STEP ALGORITHM 77 5.2 THE
PREDICTOR-CORRECTOR ALGORITHM 78 5.3 THE LARGEST STEP ALGORITHM 79 5.4
THE LONG STEP ALGORITHM 81 6. DISCUSSION 82 6.1 SELF-SCALED BARRIERS 83
6.2 MATRIX TARGETS 83 6.3 EIGENVALUE TARGETS 87 6.4 FINAL REMARKS ON THE
SEARCH DIRECTION 91 4 SELF-DUAL EMBEDDING TECHNIQUE 93 1. SELF-DUALITY
93 2. SELF-DUAL EMBEDDING 96 2.1 THE HOMOGENEOUS SELF-DUAL MODEL 96 2.2
THE EXTENDED SELF-DUAL MODEL 98 3. WEAKLY CENTERED SEQUENCES 101 4. THE
PRIMAL-DUAL MODEL 106 4.1 EXAMPLES IN SEMIDEFINITE PROGRAMMING 113 5.
EXISTENCE OF WEAKLY CENTERED SEQUENCES 122 6. DISCUSSION 127 5
PROPERTIES OF THE CENTRAL PATH 129 1. INTRODUCTION 129 2. ANALYSIS 132
3. DISCUSSION 140 6 SUPERLINEAR CONVERGENCE 143 1. A PREDICTOR-CORRECTOR
ALGORITHM 143 2. CONVERGENCE ANALYSIS 146 CONTENTS VII 3. DISCUSSION 154
7 CENTRAL REGION METHOD 157 1. WEIGHTED CENTERS 158 2. CENTRAL REGION
AND ITS NEIGHBORHOOD 163 3. GENERIC CENTRAL REGION METHOD 166 4. SECOND
ORDER SEARCH DIRECTION 171 5. THE CENTERING-PREDICTOR-CORRECTOR
ALGORITHM 173 5.1 THE PREDICTOR 173 5.2 SECOND ORDER CORRECTION 174 5.3
POLYNOMIALITY 175 6. DISCUSSION 178 REFERENCES 181 PART II LINEAR,
QUADRATIC, SEMIDEFINITE PROGRAMMING AND BEYOND 8 AN IMPLEMENTATION OF
THE HOMOGENEOUS ALGORITHM 197 ERLING D. ANDERSEN AND KNUD D. ANDERSEN 1.
INTRODUCTION 197 2. NOTATION 199 3. THE HOMOGENEOUS MODEL 200 4. THE
HOMOGENEOUS ALGORITHM 204 4.1 THE ALGORITHMIC PARAMETERS 205 4.2 THE
METHOD OF MULTIPLE CORRECTIONS 206 4.3 THE STEP SIZE 208 4.4 THE
STARTING POINT 209 4.5 THE STOPPING CRITERIA 209 5. THE SOLUTION OF THE
NEWTON EQUATION SYSTEM 211 5.1 THE SYMMETRIE LINEAR SYSTEM 212 5.2 THE
PUSH CHOLESKY 214 5.3 THE DENSE COLUMNS IN A 21 8 6. THE PARALLELIZATION
219 7. THE BASIS IDENTIFICATION PROCEDURE 219 8. THE PREPROCESSING 220
9. THE COMPUTATIONAL RESULTS 220 10. CONCLUSION 228 9 A SIMPLIFIED
CORRECTNESS PROOF FOR INTERIOR POINT ALGORITHM 233 STEPHEN A. VAVASIS
AND YINYU YE 1. INTRODUCTION 233 2. THREE CASES IN THE LIP ALGORITHM 234
3. CASE II CAN NEVER OEEUR 237 4. A SIMPLIFIED SECTION 7 240 VIII HIGH
PERFORMANCE OPTIMIZATION TECHNIQUES 10 NEW ANALYSIS OF NEWTON METHODS
FOR LCP 245 JIMING PENG, CORNELIS ROOS AND TAMDS TERLAKY 1. INTRODUCTION
245 2. PRELIMINARIES 248 3. COMPLEXITY OF THE PRIMAL-DUAL NEWTON METHOD
249 3.1 ESTIMATE OF THE PROXIMITY AFTER A DAMPED NEWTON STEP 250 3.2
THECASELLIT 1 !!, 1 252 3.3 ITERATION BOUND FOR THE PRIMAL-DUAL NEWTON
METHOD 254 4. COMPLEXITY OF FINDING A MAXIMALLY COMPLEMENTARITY SOLUTION
256 5. CONCLUDING REMARKS 261 11 NUMERICAL EVALUATION OF SDPA 267
KATSUKI FUJISAWA, MITUHIRO FUKUDA, MASAKAZU KOJIMA AND KAZUHIDE NAKATA
1. INTRODUCTION 267 2. SOME ISSUES OF THE IMPLEMENTATION OF SDPA 269 2.1
SEARCH DIRECTION 269 2.2 APPROXIMATION OF THE MINIMUM EIGENVALUE OF A
SYM- METRIE MATRIX 271 2.3 THE ALGORITHMIC FRAMEWORK OF SDPA 274 2.4
GETTING INFORMATION ON INFEASIBILITY AND UNBOUNDED- NESS 275 3. TEST
PROBLEMS 279 3.1 RANDOMLY GENERATED DENSE SEMIDEFINITE PROGRAM 279 3.2
NORM MINIMIZATION PROBLEM 279 3.3 CHEBYSHEV APPROXIMATION PROBLEM FOR A
MATRIX 280 3.4 SEMIDEFINITE PROGRAM ARISING FROM CONTROL AND SYSTEM
THEORY 280 3.5 SEMIDEFINITE PROGRAMMING RELAXATION OF THE MAXIMUM CUT
PROBLEM 281 3.6 SEMIDEFINITE PROGRAMMING RELAXATION OF THE GRAPH
EQUIPAR- TITION PROBLEM 282 3.7 SEMIDEFINITE PROGRAMMING RELAXATION OF
THE MAXIMUM CLIQUE PROBLEM 282 4. PRELIMINARY NUMERICAL EXPERIMENTS 283
5. NUMERICAL RESULTS 286 5.1 RANDOMLY GENERATED SEMIDEFINITE PROGRAM 288
5.2 NORM MINIMIZATION AND CHEBYSHEV PROBLEMS 289 5.3 CONTROL AND SYSTEM
THEORY PROBLEM 291 5.4 MAXIMUM CUT PROBLEM AND GRAPH EQUIPARTITION PROB-
LEM 292 5.5 MAXIMUM CLIQUE PROBLEM 294 6. CONCLUDING REMARKS 294 12
ROBUST MODELING OF MULTI-STAGE PORTFOLIO PROBLEMS 303 AHARON BEN-TAL,
TAMAR MARGALIT AND ARKADI NEMIROVSKI 1. INTRODUCTION 303 1.1 THE
ORIGINAL PROBLEM 303 1.2 THE CASE OF COMPLETE INFORMATION 305 1.3 DATA
UNCERTAINTY 306 CONTENTS IX 2. ROBUST COUNTERPART APPROACH TO THE
PORTFOLIO PROBLEM 307 2.1 SIMPLIFICATION OF THE ROBUST PORTFOLIO MODEL
311 2.2 DISCUSSION 314 3. SIMULATED NUMERICAL RESULTS 317 3.1 STOCHASTIC
MODEL OF THE MARKET 318 3.2 FINAL FORM OF THE ROBUST PORTFOLIO MODEL 318
3.2.1 SETUP FOR MARKET S MODEL 320 3.3 SIMULATED POLICIES AND SIMULATION
SCHEME 322 3.4 COMPUTATIONAL RESULTS 325 13 AN INTERIOR POINT SQP
PARALLEL B&B METHOD 329 EVA K. LEE AND JOHN E. MITCHELL 1. INTRODUCTION
329 2. INTERIOR-POINT BASED NONLINEAR SOLVER 330 2.1 OVERVIEW OF THE
INTERIOR-POINT SOLVER. 331 2.2 SPECIAL FEATURES WITHIN THE SQP SOLVER
332 2.2.1 SCALING OF INPUT MATRIX 333 2.2.2 HEURISTIC JUMPSTART OF (QP)
333 2.2.3 HEURISTIC MINIMUM ORDERING AND DIAGONAL AUG- MENTATION 333
2.2.4 ITERATIVE DUAL REFINEMENT 334 2.2.5 UPDATE DUAL VARIABLES OF NLP
334 3. THE NONLINEAR BRANCH-AND-BOUND SOLVER 334 4. PARALLEL
IMPLEMENTATION 337 5. NUMERICAL RESULTS 339 6. CONCLUSIONS AND CURRENT
RESEARCH 343 14 SOLVING LINEAR ORDERING PROBLEMS 349 JOHN E. MITCHELL
AND BRIAN BORCHERS 1. INTRODUCTION 349 2. THE LINEAR ORDERING PROBLEM
350 2.1 APPLICATIONS 350 2.2 MODELING THE PROBLEM 351 3. THE POLYHEDRAL
STRUCTURE OF THE LINEAR ORDERING POLYTOPE 352 4. A BASIC CUTTING PLANE
APPROACH 353 5. REFINEMENTS WITH THE INTERIOR POINT CUTTING PLANE METHOD
355 6. COMBINING THE TWO SOLVERS 356 7. COMPUTATIONAL RESULTS 357 8.
CONCLUSIONS 360 15 FINITE ELEMENT METHODS FOR SOLVING PARABOLIC INVERSE
PROBLEMS 367 YEE LO KEUNG AND JUN ZOU 1. INTRODUCTION 367 2. FINITE
ELEMENT METHOD AND ITS CONVERGENCE 369 3. UNCONSTRAINED MINIMIZATION
PROBLEMS 371 4. ARMIJO ALGORITHM 372 X HIGH PERFORMANCE OPTIMIZATION
TECHNIQUES 5. NUMERICAL EXPERIMENTS 375 16 ERROR BOUNDS FOR 383
QUADRATIC SYSTEMS ZHI-QUAN LUO AND JOS F. STURM 1. INTRODUCTION 383 2. A
SUMMARY OF ERROR BOUNDS FOR QUADRATIC SYSTEMS 385 3. NEW ERROR BOUNDS
FOR QUADRATIC SYSTEMS 390 4. CONCLUDING REMARKS 400 17 SQUARED
FUNCTIONAL SYSTEMS AND OPTIMIZATION PROBLEMS 405 YURII NESTEROV 1.
INTRODUCTION 405 2. REPRESENTATION THEOREMS 408 2.1 SUM OF SQUARES 408
2.2 SUM OF WEIGHTED SQUARES 414 2.3 FUNCTIONAL SYSTEMS WITH COMPLEX
VALUES 417 3. CONES OF NON-NEGATIVE POLYNOMIALS 422 3.1 POLYNOMIALS ON
AN INFINITE INTERVAL 422 3.2 POLYNOMIALS ON A SEMI-INFINITE INTERVAL 424
3.3 POLYNOMIALS ON A FINITE INTERVAL 425 3.3.1 POLYNOMIALS OF EVEN
DEGREE 425 3.3.2 POLYNOMIALS OF ODD DEGREE 427 3.4 TRIGONOMETRIE
POLYNOMIALS 428 3.5 NEVANLINNA-PICK PROBLEMS 429 4. DISCUSSION 431 4.1
POLYNOMIAL BOUNDS FOR A TRAJEETORY. 431 4.2 MINIMIZATION OF UNIVARIATE
POLYNOMIALS 431 4.3 MAXIMIZATION OF POLYNOMIAL FRACTIONS 432 4.4 DUAL
PROBLEMS 432 4.5 COMBINATORIAL PROBLEMS 433 4.6 MINIMIZATION OF
MULTIVARIATE POLYNOMIALS. 435 4.7 DUALITY RELATIONS 436 18 INTERIOR
POINT METHODS: CURRENT STATUS AND FUTURE DIRECTIONS 441 ROBERT M. FREUND
AND SHINJI MIZUNO 1. INTRODUCTION 441 2. INFEASIBLE INTERIOR POINT
METHODS 449 3. COMPUTATIONAL ASPECTS OF INTERIOR POINT METHODS FOR
LINEAR PROGRAMMING 451 4. HOMOGENEOUS SELF-DUAL METHODS 452 5.
SEMIDEFINITE PROGRAMMING 454 6. CONVEX PROGRAMMING AND SELF-CONCORDANCE
458 7. LINEAR AND NONLINEAR COMPLEMENTARITY PROBLEMS 461 8. SOME
THEORETICAL ISSUES RELATED TO INTERIOR POINT METHODS 462 INDEX 467
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| id | DE-604.BV013048195 |
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| institution | BVB |
| isbn | 0792360133 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008890340 |
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| open_access_boolean | |
| owner | DE-703 DE-521 |
| owner_facet | DE-703 DE-521 |
| physical | XXII, 473 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Applied optimization |
| series2 | Applied optimization |
| spelling | High performance optimization ed. by Hans Frenk ... Dordrecht [u.a.] Kluwer 2000 XXII, 473 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 33 Optimaliseren gtt Mathematical optimization Innere-Punkte-Methode (DE-588)4352322-5 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Semidefinite Optimierung (DE-588)4663806-4 gnd rswk-swf Semidefinite Optimierung (DE-588)4663806-4 s Innere-Punkte-Methode (DE-588)4352322-5 s DE-604 Konvexe Optimierung (DE-588)4137027-2 s Frenk, Hans Sonstige oth Applied optimization 33 (DE-604)BV010841718 33 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008890340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | High performance optimization Applied optimization Optimaliseren gtt Mathematical optimization Innere-Punkte-Methode (DE-588)4352322-5 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Semidefinite Optimierung (DE-588)4663806-4 gnd |
| subject_GND | (DE-588)4352322-5 (DE-588)4137027-2 (DE-588)4663806-4 |
| title | High performance optimization |
| title_auth | High performance optimization |
| title_exact_search | High performance optimization |
| title_full | High performance optimization ed. by Hans Frenk ... |
| title_fullStr | High performance optimization ed. by Hans Frenk ... |
| title_full_unstemmed | High performance optimization ed. by Hans Frenk ... |
| title_short | High performance optimization |
| title_sort | high performance optimization |
| topic | Optimaliseren gtt Mathematical optimization Innere-Punkte-Methode (DE-588)4352322-5 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Semidefinite Optimierung (DE-588)4663806-4 gnd |
| topic_facet | Optimaliseren Mathematical optimization Innere-Punkte-Methode Konvexe Optimierung Semidefinite Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008890340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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