Minimization Methods for Non-Differentiable Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1985
|
| Series: | Springer Series in Computational Mathematics
3 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (VIII, 164 p) |
| ISBN: | 9783642821189 9783642821202 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-82118-9 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423034 | ||
| 003 | DE-604 | ||
| 005 | 20180110 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1985 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642821189 |c Online |9 978-3-642-82118-9 | ||
| 020 | |a 9783642821202 |c Print |9 978-3-642-82120-2 | ||
| 024 | 7 | |a 10.1007/978-3-642-82118-9 |2 doi | |
| 035 | |a (OCoLC)1165540595 | ||
| 035 | |a (DE-599)BVBBV042423034 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 519 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Shor, Naum Zuselevich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Minimization Methods for Non-Differentiable Functions |c by Naum Zuselevich Shor |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1985 | |
| 300 | |a 1 Online-Ressource (VIII, 164 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Springer Series in Computational Mathematics |v 3 |x 0179-3632 | |
| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Systems theory | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Systems Theory, Control | |
| 650 | 4 | |a Calculus of Variations and Optimal Control; Optimization | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gradientenverfahren |0 (DE-588)4157995-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtdifferenzierbare Funktion |0 (DE-588)4326748-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Minimierung |0 (DE-588)4251074-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtdifferenzierbare Funktion |0 (DE-588)4326748-8 |D s |
| 689 | 0 | 1 | |a Gradientenverfahren |0 (DE-588)4157995-1 |D s |
| 689 | 0 | 2 | |a Minimierung |0 (DE-588)4251074-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtdifferenzierbare Funktion |0 (DE-588)4326748-8 |D s |
| 689 | 1 | 1 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 830 | 0 | |a Springer Series in Computational Mathematics |v 3 |w (DE-604)BV000012004 |9 3 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-82118-9 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858451 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153098284826624 |
|---|---|
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03905nmm a2200601zcb4500</leader><controlfield tag="001">BV042423034</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180110 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1985 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642821189</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-82118-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642821202</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-82120-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-82118-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165540595</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423034</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shor, Naum Zuselevich</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Minimization Methods for Non-Differentiable Functions</subfield><subfield code="c">by Naum Zuselevich Shor</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1985</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 164 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Springer Series in Computational Mathematics</subfield><subfield code="v">3</subfield><subfield code="x">0179-3632</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Systems theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Systems Theory, Control</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Calculus of Variations and Optimal Control; Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gradientenverfahren</subfield><subfield code="0">(DE-588)4157995-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtdifferenzierbare Funktion</subfield><subfield code="0">(DE-588)4326748-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Minimierung</subfield><subfield code="0">(DE-588)4251074-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtdifferenzierbare Funktion</subfield><subfield code="0">(DE-588)4326748-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Gradientenverfahren</subfield><subfield code="0">(DE-588)4157995-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Minimierung</subfield><subfield code="0">(DE-588)4251074-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtdifferenzierbare Funktion</subfield><subfield code="0">(DE-588)4326748-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Springer Series in Computational Mathematics</subfield><subfield code="v">3</subfield><subfield code="w">(DE-604)BV000012004</subfield><subfield code="9">3</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-82118-9</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858451</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| 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 |
| oclc_num | 1165540595 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 164 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| 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 |