Foundations of mathematical optimization: convex analysis without linearity
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
388 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 582 S. |
| ISBN: | 0792344243 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1. GENERAL OPTIMALITY
1.1. $ subgradients and $ supergradients 1
1.2. Duality 16
1.3. Optimization problems with constraints 21
1.4. ^ convex sets 23
1.5. $ convexity in linear spaces 28
1.6. ^ separation 37
1.7. Constraints of multifunction type 40
1.8. Polarity and duality 50
Chapter 2. OPTIMIZATION IN METRIC SPACES
2.1. $ convex functions in topological and metric spaces 56
2.2. Ekeland Variational Principle and existence of $£ subgradients 61
2.3. Well conditioned functions 67
2.4. Duality in metric spaces 76
2.5. Local minima 97
2.6. Local subgradients, supergradients and gradients 110
2.7. Optimization with constraints. Outer and inner approximations in
metric spaces 130
2.8. Frechet differentiability of real valued functions 135
2.9. 3? subgradients, $ supergradients and ^ gradients of superpositions 141
2.10. On differentiability in normed spaces 150
Chapter 3. MULTIFUNCTION AND MARGINAL FUNCTIONS IN METRIC
SPACES
3.1. Lower semicontinuity of marginal functions 171
3.2. Local optimization problems 184
3.3. Exact penalties 197
3.4. Almost lower semi continuous multifunctioiis 206
3.5. Behaviour of minimal sets as multifunctions 212
3.6. Behaviour of ^ subdifferentials as a multifunction 223
Chapter 4. WELL POSEDNESS AND WEAK WELL POSEDNESS IN
BANACH SPACES
4.1. Convexity with respect to linear continuous functionals 231
4.2. Well posed problems for linear functionals on convex sets 240
4.3. Streams with bounded bases 248
v
vi Contents
4.4. Weakly well posed problems 254
4.5. Well posedness and weak well posedness and the drop property
for unbounded sets 261
4.6. Uniformly well posed problems 273
4.7. Uniformly weakly well posed problems 287
Chapter 5. DUALITY IN BANACH AND HILBERT SPACES.
REGULARIZATION
5.1. Fenchel conjugate functions in Banach spaces 294
5.2. Quadratic regularization in Hilbert spaces 296
5.3. The density of the points of differentiability of convex functions 305
Chapter 6.NECESSARY CONDITIONS FOR OPTIMALITY AND LOCAL
OPTIMALITY IN NORMED SPACES.
6.1. Inner and outer conical approximation in normed spaces 313
6.2. Upper and lower limits of multifunctions in topological spaces 336
6.3. Dubovitzkii Milyutin theorem in locally convex spaces 341
6.4. Dolecki approximations 364
6.5. Necessary conditions of the first order for local optimality 374
Chapter 7.POLYNOMIALS. NECESSARY AND SUFFICIENT CONDITIONS
OF OPTIMALITY OF HIGHER ORDER
7.1. Polynomials. Higher order necessary and sufficient conditions of
optimality without constraints 390
7.2. Higher order necessary and sufficient conditions of optimality with
constraints 396
7.3. Method of reduction of constraints 403
Chapter 8. NONDIFFERENTIABLE OPTIMIZATION
8.1. DC functions and the approximation of the first order by DC functions. 412
8.2. Construction of universal derivative 432
8.3. Quasidifferentiable functions 441
8.4. Point derivatives and critical points 448
8.5. Regular points and the locally open range of quasidifferentiable
functions 455
8.6. Higher order derivatives for quasidifferentiable functions 458
8.7. Optimality conditions in quasidifferentiable optimization 464
Chapter 9. NUMERICAL ASPECTS
9.1. The $ bundle method 469
9.2. The subgradient method 475
9.3. The Karush Kuhn Tucker system 483
9.4. The nonlinear complementarity problem 486
Contents vii
9.5. The continuous set covering problem 491
Chapter 10. VECTOR OPTIMIZATION
10.1. Pareto minima and maxima 497
10.2. Necessary conditions of optimality 512
10.3. Sufficient conditions for local Pareto points 517
10.4. Duality theory in vector lattices 522
10.5. Duality theory with Pareto sets 529
10.6. S subdifferentiability in normed spaces 539
10.7. Lower semi continuity of marginal functions 543
Bibliography 551
Subject index 571
Author index 577
List of symbols 581
|
| any_adam_object | 1 |
| author | Pallaschke, Diethard Rolewicz, Stefan |
| author_facet | Pallaschke, Diethard Rolewicz, Stefan |
| author_role | aut aut |
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| bvnumber | BV011561999 |
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| callnumber-raw | QA331.5.P34 1997 |
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| dewey-full | 515/.8 515/.821 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 515/.8 21 |
| dewey-search | 515/.8 515/.8 21 |
| dewey-sort | 3515 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011561999 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:53Z |
| institution | BVB |
| isbn | 0792344243 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007785690 |
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| physical | XII, 582 S. |
| publishDate | 1997 |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Pallaschke, Diethard Verfasser aut Foundations of mathematical optimization convex analysis without linearity by Diethard Pallaschke and Stefan Rolewicz Dordrecht [u.a.] Kluwer 1997 XII, 582 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 388 Fonctions convexes ram Convex functions Convex sets Mathematical optimization Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Konvexe Analysis (DE-588)4138566-4 s Unendlichdimensionaler Raum (DE-588)4207852-0 s Rolewicz, Stefan Verfasser aut Mathematics and its applications 388 (DE-604)BV008163334 388 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007785690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pallaschke, Diethard Rolewicz, Stefan Foundations of mathematical optimization convex analysis without linearity Mathematics and its applications Fonctions convexes ram Convex functions Convex sets Mathematical optimization Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Konvexe Analysis (DE-588)4138566-4 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4207852-0 (DE-588)4138566-4 (DE-588)4043664-0 |
| title | Foundations of mathematical optimization convex analysis without linearity |
| title_auth | Foundations of mathematical optimization convex analysis without linearity |
| title_exact_search | Foundations of mathematical optimization convex analysis without linearity |
| title_full | Foundations of mathematical optimization convex analysis without linearity by Diethard Pallaschke and Stefan Rolewicz |
| title_fullStr | Foundations of mathematical optimization convex analysis without linearity by Diethard Pallaschke and Stefan Rolewicz |
| title_full_unstemmed | Foundations of mathematical optimization convex analysis without linearity by Diethard Pallaschke and Stefan Rolewicz |
| title_short | Foundations of mathematical optimization |
| title_sort | foundations of mathematical optimization convex analysis without linearity |
| title_sub | convex analysis without linearity |
| topic | Fonctions convexes ram Convex functions Convex sets Mathematical optimization Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Konvexe Analysis (DE-588)4138566-4 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Fonctions convexes Convex functions Convex sets Mathematical optimization Unendlichdimensionaler Raum Konvexe Analysis Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007785690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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