Stochastic optimization methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 340 S. graph. Darst. 235 mm x 155 mm, 680 gr. |
| ISBN: | 9783540794578 |
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| 245 | 1 | 0 | |a Stochastic optimization methods |c Kurt Marti |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIII, 340 S. |b graph. Darst. |c 235 mm x 155 mm, 680 gr. | ||
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Record in the Search Index
| _version_ | 1804137991999848448 |
|---|---|
| adam_text | KURT MARTI STOCHASTIC OPTIMIZATION METHODS SECOND EDITION 4Y SPRINGER
CONTENTS PART I BASIC STOCHASTIC OPTIMIZATION METHODS 1 DECISION/CONTROL
UNDER STOCHASTIC UNCERTAINTY 3 1.1 INTRODUCTION 3 1.2 DETERMINISTIC
SUBSTITUTE PROBLEMS: BASIC FORMULATION 5 1.2.1 MINIMUM OR BOUNDED
EXPECTED COSTS 6 1.2.2 MINIMUM OR BOUNDED MAXIMUM COSTS (WORST CASE) 8 2
DETERMINISTIC SUBSTITUTE PROBLEMS IN OPTIMAL DECISION UNDER STOCHASTIC
UNCERTAINTY 9 2.1 OPTIMUM DESIGN PROBLEMS WITH RANDOM PARAMETERS 9 2.1.1
DETERMINISTIC SUBSTITUTE PROBLEMS IN OPTIMAL DESIGN 13 2.1.2
DETERMINISTIC SUBSTITUTE PROBLEMS IN QUALITY ENGINEERING 16 2.2 BASIC
PROPERTIES OF SUBSTITUTE PROBLEMS 18 2.3 APPROXIMATIONS OF DETERMINISTIC
SUBSTITUTE PROBLEMS IN OPTIMAL DESIGN 19 2.3.1 APPROXIMATION OF THE LOSS
FUNCTION 20 2.3.2 REGRESSION TECHNIQUES, MODEL FITTING, RSM 22 2.3.3
TAYLOR EXPANSION METHODS 26 2.4 APPLICATIONS TO PROBLEMS IN QUALITY
ENGINEERING 29 2.5 APPROXIMATION OF PROBABILITIES: PROBABILITY
INEQUALITIES 30 2.5.1 BONFERRONI-TYPE INEQUALITIES 31 2.5.2
TSCHEBYSCHEFF-TYPE INEQUALITIES 32 2.5.3 FIRST ORDER RELIABILITY METHODS
(FORM) 37 X CONTENTS PART II DIFFERENTIATION METHODS DIFFERENTIATION
METHODS FOR PROBABILITY AND RISK FUNCTIONS 43 3.1 INTRODUCTION 43 3.2
TRANSFORMATION METHOD: DIFFERENTIATION BY USING AN INTEGRAL
TRANSFORMATION 46 3.2.1 REPRESENTATION OF THE DERIVATIVES BY SURFACE
INTEGRALS.. 51 3.3 THE DIFFERENTIATION OF STRUCTURAL RELIABILITIES 54
3.4 EXTENSIONS 57 3.4.1 MORE GENERAL RESPONSE (STATE) FUNCTIONS 57 3.5
COMPUTATION OF PROBABILITIES AND ITS DERIVATIVES BY ASYMPTOTIC
EXPANSIONS OF INTEGRAL OF LAPLACE TYPE 62 3.5.1 COMPUTATION OF
PROBABILITIES OF STRUCTURAL FAILURE AND THEIR DERIVATIVES 62 3.5.2
NUMERICAL COMPUTATION OF DERIVATIVES OF THE PROBABILITY FUNCTIONS
ARISING IN CHANCE CONSTRAINED PROGRAMMING 66 3.6 INTEGRAL
REPRESENTATIONS OF THE PROBABILITY FUNCTION P(X) AND ITS DERIVATIVES 72
3.7 ORTHOGONAL FUNCTION SERIES EXPANSIONS I: EXPANSIONS IN HERMITE
FUNCTIONS, CASE M = 1 75 3.7.1 INTEGRALS OVER THE BASIS FUNCTIONS AND
THE COEFFICIENTS OF THE ORTHOGONAL SERIES 79 3.7.2
ESTIMATION/APPROXIMATION OF P(X) AND ITS DERIVATIVES . 82 3.7.3 THE
INTEGRATED SQUARE ERROR (ISE) OF DETERMINISTIC APPROXIMATIONS 88 3.8
ORTHOGONAL FUNCTION SERIES EXPANSIONS II: EXPANSIONS IN HERMITE
FUNCTIONS, CASE M 1 89 3.9 ORTHOGONAL FUNCTION SERIES EXPANSIONS III:
EXPANSIONS IN TRIGONOMETRIC, LEGENDRE AND LAGUERRE SERIES 91 3.9.1
EXPANSIONS IN TRIGONOMETRIC AND LEGENDRE SERIES 92 3.9.2 EXPANSIONS IN
LAGUERRE SERIES 92 PART III DETERMINISTIC DESCENT DIRECTIONS 4
DETERMINISTIC DESCENT DIRECTIONS AND EFFICIENT POINTS 95 4.1 CONVEX
APPROXIMATION , 95 4.1.1 APPROXIMATIVE CONVEX OPTIMIZATION PROBLEM 99
4.2 COMPUTATION OF DESCENT DIRECTIONS IN CASE OF NORMAL DISTRIBUTIONS
101 4.2.1 DESCENT DIRECTIONS OF. CONVEX PROGRAMS 105 4.2.2 SOLUTION OF
THE AUXILIARY PROGRAMS 108 4.3 EFFICIENT SOLUTIONS (POINTS) 113 4.3.1
NECESSARY OPTIMALITY CONDITIONS WITHOUT GRADIENTS ... 116 CONTENTS XI
4.3.2 EXISTENCE OF FEASIBLE DESCENT DIRECTIONS IN NON-EFFICIENT
SOLUTIONS OF (4.9A), (4.9B) 117 4.4 DESCENT DIRECTIONS IN CASE OF
ELLIPTICALLY CONTOURED DISTRIBUTIONS 118 4.5 CONSTRUCTION OF DESCENT
DIRECTIONS BY USING QUADRATIC APPROXIMATIONS OF THE LOSS FUNCTION 121
PART IV SEMI-STOCHASTIC APPROXIMATION METHODS 5 RSM-BASED STOCHASTIC
GRADIENT PROCEDURES 129 5.1 INTRODUCTION 129 5.2 GRADIENT ESTIMATION
USING THE RESPONSE SURFACE METHODOLOGY (RSM) 131 5.2.1 THE TWO PHASES OF
RSM 134 5.2.2 THE MEAN SQUARE ERROR OF THE GRADIENT ESTIMATOR .... 138
5.3 ESTIMATION OF THE MEAN SQUARE (MEAN FUNCTIONAL) ERROR 142 5.3.1 THE
ARGUMENT CASE 143 5.3.2 THE CRITERIAL CASE 147 5.4 CONVERGENCE BEHAVIOR
OF HYBRID STOCHASTIC APPROXIMATION METHODS 147 5.4.1 ASYMPTOTICALLY
CORRECT RESPONSE SURFACE MODEL 148 5.4.2 BIASED RESPONSE SURFACE MODEL
150 5.5 CONVERGENCE RATES OF HYBRID STOCHASTIC APPROXIMATION PROCEDURES
153 5.5.1 FIXED RATE OF STOCHASTIC AND DETERMINISTIC STEPS 158 5.5.2
LOWER BOUNDS FOR THE MEAN SQUARE ERROR 169 5.5.3 DECREASING RATE OF
STOCHASTIC STEPS 173 6 STOCHASTIC APPROXIMATION METHODS WITH CHANGING
ERROR VARIANCES 177 6.1 INTRODUCTION 177 6.2 SOLUTION OF OPTIMALITY
CONDITIONS 178 6.3 GENERAL ASSUMPTIONS AND NOTATIONS 179 6.3.1
INTERPRETATION OF THE ASSUMPTIONS 181 6.3.2 NOTATIONS AND ABBREVIATIONS
IN THIS CHAPTER 182 6.4 PRELIMINARY RESULTS 183 6.4.1 ESTIMATION OF
THE QUADRATIC ERROR 183 6.4.2 CONSIDERATION OF THE WEIGHTED ERROR
SEQUENCE 185 6.4.3 FURTHER PRELIMINARY RESULTS 188 6.5 GENERAL
CONVERGENCE RESULTS 190 6.5.1 CONVERGENCE WITH PROBABILITY ONE 190 6.5.2
CONVERGENCE IN THE MEAN . 192 6.5.3 CONVERGENCE IN DISTRIBUTION 195 6.6
REALIZATION OF SEARCH DIRECTIONS Y N 204 6.6.1 ESTIMATION OF G* 209 XII
CONTENTS 6.6.2 UPDATE OF THE JACOBIAN 210 6.6.3 ESTIMATION OF ERROR
VARIANCES 216 6.7 REALIZATION OF ADAPTIVE STEP SIZES 220 6.7.1 OPTIMAL
MATRIX STEP SIZES 221 6.7.2 ADAPTIVE SCALAR STEP SIZE 227 6.8 A SPECIAL
CLASS OF ADAPTIVE SCALAR STEP SIZES 236 6.8.1 CONVERGENCE PROPERTIES 237
6.8.2 EXAMPLES FOR THE FUNCTION Q N (R) 241 6.8.3 OPTIMAL SEQUENCE (W N
) 247 6.8.4 SEQUENCE (K N ) 247 PART V RELIABILITY ANALYSIS OF
STRUCTURES/SYSTEMS 7 COMPUTATION OF PROBABILITIES OF SURVIVAL/FAILURE BY
MEANS OF PIECEWISE LINEARIZATION OF THE STATE FUNCTION 253 7.1
INTRODUCTION 253 7.2 THE STATE FUNCTION S* 256 7.2.1 CHARACTERIZATION OF
SAFE STATES 258 7.3 PROBABILITY OF SAFETY/SURVIVAL 259 7.4 APPROXIMATION
I OF P S ,PF. FORM 262 7.4.1 THE ORIGIN OF IR LIES IN THE TRANSFORMED
SAFE DOMAIN _. 262 7.4.2 THE ORIGIN OF IR LIES IN THE TRANSFORMED
FAILURE DOMAIN 266 7.4.3 THE ORIGIN OF IR LIES ON THE LIMIT STATE
SURFACE 268 7.4.4 APPROXIMATION OF RELIABILITY CONSTRAINTS 269 7.5
APPROXIMATION II OF P S ,PF. POLYHEDRAL APPROXIMATION OF THE SAFE/UNSAFE
DOMAIN 270 7.5.1 POLYHEDRAL APPROXIMATION 273 7.6 COMPUTATION OF THE
BOUNDARY POINTS 279 7.6.1 STATE FUNCTION S* REPRESENTED BY PROBLEM A 280
7.6.2 STATE FUNCTION S* REPRESENTED BY PROBLEM B 280 7.7 COMPUTATION OF
THE APPROXIMATE PROBABILITY FUNCTIONS 282 7.7.1 PROBABILITY
INEQUALITIES 282 7.7.2 DISCRETIZATION METHODS . 289 7.7.3 CONVERGENT
SEQUENCES OF DISCRETE DISTRIBUTIONS 293 PART VI APPENDIX A SEQUENCES,
SERIES AND PRODUCTS 301 A.I MEAN VALUE THEOREMS FOR DETERMINISTIC
SEQUENCES 301 A.2 ITERATIVE SOLUTION OF A LYAPUNOV MATRIX EQUATION 309
CONTENTS XIII B CONVERGENCE THEOREMS FOR STOCHASTIC SEQUENCES 313 B.I A
CONVERGENCE RESULT OF ROBBINS-SIEGMUND 313 B.I.I CONSEQUENCES 313 B.2
CONVERGENCE IN THE MEAN 316 B.3 THE STRONG LAW OF LARGE NUMBERS FOR
DEPENDENT MATRIX SEQUENCES 318 B.4 A CENTRAL LIMIT THEOREM FOR DEPENDENT
VECTOR SEQUENCES. ... 319 C TOOLS FROM MATRIX CALCULUS 321 C.I
MISCELLANEOUS 321 C.2 THE V. MISES-PROCEDURE IN CASE OF ERRORS 322
REFERENCES 327 INDEX 335
|
| adam_txt |
KURT MARTI STOCHASTIC OPTIMIZATION METHODS SECOND EDITION 4Y SPRINGER
CONTENTS PART I BASIC STOCHASTIC OPTIMIZATION METHODS 1 DECISION/CONTROL
UNDER STOCHASTIC UNCERTAINTY 3 1.1 INTRODUCTION 3 1.2 DETERMINISTIC
SUBSTITUTE PROBLEMS: BASIC FORMULATION 5 1.2.1 MINIMUM OR BOUNDED
EXPECTED COSTS 6 1.2.2 MINIMUM OR BOUNDED MAXIMUM COSTS (WORST CASE) 8 2
DETERMINISTIC SUBSTITUTE PROBLEMS IN OPTIMAL DECISION UNDER STOCHASTIC
UNCERTAINTY 9 2.1 OPTIMUM DESIGN PROBLEMS WITH RANDOM PARAMETERS 9 2.1.1
DETERMINISTIC SUBSTITUTE PROBLEMS IN OPTIMAL DESIGN 13 2.1.2
DETERMINISTIC SUBSTITUTE PROBLEMS IN QUALITY ENGINEERING 16 2.2 BASIC
PROPERTIES OF SUBSTITUTE PROBLEMS 18 2.3 APPROXIMATIONS OF DETERMINISTIC
SUBSTITUTE PROBLEMS IN OPTIMAL DESIGN 19 2.3.1 APPROXIMATION OF THE LOSS
FUNCTION 20 2.3.2 REGRESSION TECHNIQUES, MODEL FITTING, RSM 22 2.3.3
TAYLOR EXPANSION METHODS ' 26 2.4 APPLICATIONS TO PROBLEMS IN QUALITY
ENGINEERING 29 2.5 APPROXIMATION OF PROBABILITIES: PROBABILITY
INEQUALITIES 30 2.5.1 BONFERRONI-TYPE INEQUALITIES 31 2.5.2
TSCHEBYSCHEFF-TYPE INEQUALITIES 32 2.5.3 FIRST ORDER RELIABILITY METHODS
(FORM) 37 X CONTENTS PART II DIFFERENTIATION METHODS DIFFERENTIATION
METHODS FOR PROBABILITY AND RISK FUNCTIONS 43 3.1 INTRODUCTION 43 3.2
TRANSFORMATION METHOD: DIFFERENTIATION BY USING AN INTEGRAL
TRANSFORMATION 46 3.2.1 REPRESENTATION OF THE DERIVATIVES BY SURFACE
INTEGRALS. 51 3.3 THE DIFFERENTIATION OF STRUCTURAL RELIABILITIES 54
3.4 EXTENSIONS 57 3.4.1 MORE GENERAL RESPONSE (STATE) FUNCTIONS 57 3.5
COMPUTATION OF PROBABILITIES AND ITS DERIVATIVES BY ASYMPTOTIC
EXPANSIONS OF INTEGRAL OF LAPLACE TYPE 62 3.5.1 COMPUTATION OF
PROBABILITIES OF STRUCTURAL FAILURE AND THEIR DERIVATIVES 62 3.5.2
NUMERICAL COMPUTATION OF DERIVATIVES OF THE PROBABILITY FUNCTIONS
ARISING IN CHANCE CONSTRAINED PROGRAMMING 66 3.6 INTEGRAL
REPRESENTATIONS OF THE PROBABILITY FUNCTION P(X) AND ITS DERIVATIVES 72
3.7 ORTHOGONAL FUNCTION SERIES EXPANSIONS I: EXPANSIONS IN HERMITE
FUNCTIONS, CASE M = 1 75 3.7.1 INTEGRALS OVER THE BASIS FUNCTIONS AND
THE COEFFICIENTS OF THE ORTHOGONAL SERIES 79 3.7.2
ESTIMATION/APPROXIMATION OF P(X) AND ITS DERIVATIVES . 82 3.7.3 THE
INTEGRATED SQUARE ERROR (ISE) OF DETERMINISTIC APPROXIMATIONS 88 3.8
ORTHOGONAL FUNCTION SERIES EXPANSIONS II: EXPANSIONS IN HERMITE
FUNCTIONS, CASE M 1 89 3.9 ORTHOGONAL FUNCTION SERIES EXPANSIONS III:
EXPANSIONS IN TRIGONOMETRIC, LEGENDRE AND LAGUERRE SERIES 91 3.9.1
EXPANSIONS IN TRIGONOMETRIC AND LEGENDRE SERIES 92 3.9.2 EXPANSIONS IN
LAGUERRE SERIES 92 PART III DETERMINISTIC DESCENT DIRECTIONS 4
DETERMINISTIC DESCENT DIRECTIONS AND EFFICIENT POINTS 95 4.1 CONVEX
APPROXIMATION , 95 4.1.1 APPROXIMATIVE CONVEX OPTIMIZATION PROBLEM 99
4.2 COMPUTATION OF DESCENT DIRECTIONS IN CASE OF NORMAL DISTRIBUTIONS
101 4.2.1 DESCENT DIRECTIONS OF. CONVEX PROGRAMS 105 4.2.2 SOLUTION OF
THE AUXILIARY PROGRAMS 108 4.3 EFFICIENT SOLUTIONS (POINTS) 113 4.3.1
NECESSARY OPTIMALITY CONDITIONS WITHOUT GRADIENTS . 116 CONTENTS XI
4.3.2 EXISTENCE OF FEASIBLE DESCENT DIRECTIONS IN NON-EFFICIENT
SOLUTIONS OF (4.9A), (4.9B) 117 4.4 DESCENT DIRECTIONS IN CASE OF
ELLIPTICALLY CONTOURED DISTRIBUTIONS 118 4.5 CONSTRUCTION OF DESCENT
DIRECTIONS BY USING QUADRATIC APPROXIMATIONS OF THE LOSS FUNCTION 121
PART IV SEMI-STOCHASTIC APPROXIMATION METHODS 5 RSM-BASED STOCHASTIC
GRADIENT PROCEDURES 129 5.1 INTRODUCTION 129 5.2 GRADIENT ESTIMATION
USING THE RESPONSE SURFACE METHODOLOGY (RSM) 131 5.2.1 THE TWO PHASES OF
RSM 134 5.2.2 THE MEAN SQUARE ERROR OF THE GRADIENT ESTIMATOR . 138
5.3 ESTIMATION OF THE MEAN SQUARE (MEAN FUNCTIONAL) ERROR 142 5.3.1 THE
ARGUMENT CASE 143 5.3.2 THE CRITERIAL CASE 147 5.4 CONVERGENCE BEHAVIOR
OF HYBRID STOCHASTIC APPROXIMATION METHODS 147 5.4.1 ASYMPTOTICALLY
CORRECT RESPONSE SURFACE MODEL 148 5.4.2 BIASED RESPONSE SURFACE MODEL
150 5.5 CONVERGENCE RATES OF HYBRID STOCHASTIC APPROXIMATION PROCEDURES
153 5.5.1 FIXED RATE OF STOCHASTIC AND DETERMINISTIC STEPS 158 5.5.2
LOWER BOUNDS FOR THE MEAN SQUARE ERROR 169 5.5.3 DECREASING RATE OF
STOCHASTIC STEPS 173 6 STOCHASTIC APPROXIMATION METHODS WITH CHANGING
ERROR VARIANCES 177 6.1 INTRODUCTION 177 6.2 SOLUTION OF OPTIMALITY
CONDITIONS 178 6.3 GENERAL ASSUMPTIONS AND NOTATIONS 179 6.3.1
INTERPRETATION OF THE ASSUMPTIONS 181 6.3.2 NOTATIONS AND ABBREVIATIONS
IN THIS CHAPTER 182 6.4 PRELIMINARY RESULTS ' 183 6.4.1 ESTIMATION OF
THE QUADRATIC ERROR 183 6.4.2 CONSIDERATION OF THE WEIGHTED ERROR
SEQUENCE 185 6.4.3 FURTHER PRELIMINARY RESULTS 188 6.5 GENERAL
CONVERGENCE RESULTS 190 6.5.1 CONVERGENCE WITH PROBABILITY ONE 190 6.5.2
CONVERGENCE IN THE MEAN'. 192 6.5.3 CONVERGENCE IN DISTRIBUTION 195 6.6
REALIZATION OF SEARCH DIRECTIONS Y N 204 6.6.1 ESTIMATION OF G* 209 XII
CONTENTS 6.6.2 UPDATE OF THE JACOBIAN 210 6.6.3 ESTIMATION OF ERROR
VARIANCES 216 6.7 REALIZATION OF ADAPTIVE STEP SIZES 220 6.7.1 OPTIMAL
MATRIX STEP SIZES 221 6.7.2 ADAPTIVE SCALAR STEP SIZE 227 6.8 A SPECIAL
CLASS OF ADAPTIVE SCALAR STEP SIZES 236 6.8.1 CONVERGENCE PROPERTIES 237
6.8.2 EXAMPLES FOR THE FUNCTION Q N (R) 241 6.8.3 OPTIMAL SEQUENCE (W N
) 247 6.8.4 SEQUENCE (K N ) 247 PART V RELIABILITY ANALYSIS OF
STRUCTURES/SYSTEMS 7 COMPUTATION OF PROBABILITIES OF SURVIVAL/FAILURE BY
MEANS OF PIECEWISE LINEARIZATION OF THE STATE FUNCTION 253 7.1
INTRODUCTION 253 7.2 THE STATE FUNCTION S* 256 7.2.1 CHARACTERIZATION OF
SAFE STATES 258 7.3 PROBABILITY OF SAFETY/SURVIVAL 259 7.4 APPROXIMATION
I OF P S ,PF. FORM 262 7.4.1 THE ORIGIN OF IR" LIES IN THE TRANSFORMED
SAFE DOMAIN _. 262 7.4.2 THE ORIGIN OF IR" LIES IN THE TRANSFORMED
FAILURE DOMAIN 266 7.4.3 THE ORIGIN OF IR" LIES ON THE LIMIT STATE
SURFACE 268 7.4.4 APPROXIMATION OF RELIABILITY CONSTRAINTS 269 7.5
APPROXIMATION II OF P S ,PF. POLYHEDRAL APPROXIMATION OF THE SAFE/UNSAFE
DOMAIN 270 7.5.1 POLYHEDRAL APPROXIMATION 273 7.6 COMPUTATION OF THE
BOUNDARY POINTS 279 7.6.1 STATE FUNCTION S* REPRESENTED BY PROBLEM A 280
7.6.2 STATE FUNCTION S* REPRESENTED BY PROBLEM B 280 7.7 COMPUTATION OF
THE APPROXIMATE PROBABILITY FUNCTIONS 282 7.7.1 PROBABILITY
INEQUALITIES' 282 7.7.2 DISCRETIZATION METHODS '. 289 7.7.3 CONVERGENT
SEQUENCES OF DISCRETE DISTRIBUTIONS 293 PART VI APPENDIX A SEQUENCES,
SERIES AND PRODUCTS 301 A.I MEAN VALUE THEOREMS FOR DETERMINISTIC
SEQUENCES 301 A.2 ITERATIVE SOLUTION OF A LYAPUNOV MATRIX EQUATION 309
CONTENTS XIII B CONVERGENCE THEOREMS FOR STOCHASTIC SEQUENCES 313 B.I A
CONVERGENCE RESULT OF ROBBINS-SIEGMUND 313 B.I.I CONSEQUENCES 313 B.2
CONVERGENCE IN THE MEAN 316 B.3 THE STRONG LAW OF LARGE NUMBERS FOR
DEPENDENT MATRIX SEQUENCES 318 B.4 A CENTRAL LIMIT THEOREM FOR DEPENDENT
VECTOR SEQUENCES. . 319 C TOOLS FROM MATRIX CALCULUS 321 C.I
MISCELLANEOUS 321 C.2 THE V. MISES-PROCEDURE IN CASE OF ERRORS 322
REFERENCES 327 INDEX 335 |
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| author | Marti, Kurt 1943- |
| author_GND | (DE-588)115845690 |
| author_facet | Marti, Kurt 1943- |
| author_role | aut |
| author_sort | Marti, Kurt 1943- |
| author_variant | k m km |
| building | Verbundindex |
| bvnumber | BV035051824 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.32 |
| callnumber-search | T57.32 |
| callnumber-sort | T 257.32 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 424 |
| ctrlnum | (OCoLC)227032487 (DE-599)DNB989188388 |
| dewey-full | 519.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.62 |
| dewey-search | 519.62 |
| dewey-sort | 3519.62 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035051824 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:56:52Z |
| indexdate | 2024-07-09T21:21:06Z |
| institution | BVB |
| isbn | 9783540794578 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016720511 |
| oclc_num | 227032487 |
| open_access_boolean | |
| owner | DE-384 DE-706 DE-20 DE-91G DE-BY-TUM |
| owner_facet | DE-384 DE-706 DE-20 DE-91G DE-BY-TUM |
| physical | XIII, 340 S. graph. Darst. 235 mm x 155 mm, 680 gr. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Marti, Kurt 1943- Verfasser (DE-588)115845690 aut Stochastic optimization methods Kurt Marti 2. ed. Berlin [u.a.] Springer 2008 XIII, 340 S. graph. Darst. 235 mm x 155 mm, 680 gr. txt rdacontent n rdamedia nc rdacarrier Mathematical optimization Stochastic processes Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-79458-5 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016720511&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marti, Kurt 1943- Stochastic optimization methods Mathematical optimization Stochastic processes Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4057625-5 |
| title | Stochastic optimization methods |
| title_auth | Stochastic optimization methods |
| title_exact_search | Stochastic optimization methods |
| title_exact_search_txtP | Stochastic optimization methods |
| title_full | Stochastic optimization methods Kurt Marti |
| title_fullStr | Stochastic optimization methods Kurt Marti |
| title_full_unstemmed | Stochastic optimization methods Kurt Marti |
| title_short | Stochastic optimization methods |
| title_sort | stochastic optimization methods |
| topic | Mathematical optimization Stochastic processes Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Mathematical optimization Stochastic processes Stochastische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016720511&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT martikurt stochasticoptimizationmethods |