Minimization Methods for Non-Differentiable Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1985
|
| Schriftenreihe: | Springer Series in Computational Mathematics
3 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In recent years much attention has been given to the development of automatic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in mathematical software packages for automatic systems of various levels and purposes. Methods for minimizing functions with discontinuous gradients are gaining in importance and the experts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the construction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are differentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the subgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods |
| Beschreibung: | 1 Online-Ressource (VIII, 164 p) |
| ISBN: | 9783642821189 9783642821202 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-82118-9 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Shor, Naum Zuselevich |
| author_facet | Shor, Naum Zuselevich |
| author_role | aut |
| author_sort | Shor, Naum Zuselevich |
| author_variant | n z s nz nzs |
| building | Verbundindex |
| bvnumber | BV042423034 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165540595 (DE-599)BVBBV042423034 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-82118-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423034 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642821189 9783642821202 |
| issn | 0179-3632 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858451 |
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| physical | 1 Online-Ressource (VIII, 164 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1985 |
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| publisher | Springer Berlin Heidelberg |
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| series | Springer Series in Computational Mathematics |
| series2 | Springer Series in Computational Mathematics |
| spelling | Shor, Naum Zuselevich Verfasser aut Minimization Methods for Non-Differentiable Functions by Naum Zuselevich Shor Berlin, Heidelberg Springer Berlin Heidelberg 1985 1 Online-Ressource (VIII, 164 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 3 0179-3632 In recent years much attention has been given to the development of automatic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in mathematical software packages for automatic systems of various levels and purposes. Methods for minimizing functions with discontinuous gradients are gaining in importance and the experts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the construction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are differentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the subgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd rswk-swf Gradientenverfahren (DE-588)4157995-1 gnd rswk-swf Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd rswk-swf Minimierung (DE-588)4251074-0 gnd rswk-swf Nichtdifferenzierbare Funktion (DE-588)4326748-8 s Gradientenverfahren (DE-588)4157995-1 s Minimierung (DE-588)4251074-0 s 1\p DE-604 Optimierung (DE-588)4043664-0 s 2\p DE-604 Springer Series in Computational Mathematics 3 (DE-604)BV000012004 3 https://doi.org/10.1007/978-3-642-82118-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shor, Naum Zuselevich Minimization Methods for Non-Differentiable Functions Springer Series in Computational Mathematics Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Minimierung (DE-588)4251074-0 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4157995-1 (DE-588)4326748-8 (DE-588)4251074-0 |
| title | Minimization Methods for Non-Differentiable Functions |
| title_auth | Minimization Methods for Non-Differentiable Functions |
| title_exact_search | Minimization Methods for Non-Differentiable Functions |
| title_full | Minimization Methods for Non-Differentiable Functions by Naum Zuselevich Shor |
| title_fullStr | Minimization Methods for Non-Differentiable Functions by Naum Zuselevich Shor |
| title_full_unstemmed | Minimization Methods for Non-Differentiable Functions by Naum Zuselevich Shor |
| title_short | Minimization Methods for Non-Differentiable Functions |
| title_sort | minimization methods for non differentiable functions |
| topic | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Minimierung (DE-588)4251074-0 gnd |
| topic_facet | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung Gradientenverfahren Nichtdifferenzierbare Funktion Minimierung |
| url | https://doi.org/10.1007/978-3-642-82118-9 |
| volume_link | (DE-604)BV000012004 |
| work_keys_str_mv | AT shornaumzuselevich minimizationmethodsfornondifferentiablefunctions |