A derivative-free descent method in set optimization
Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical meth...
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| Published in: | Computational optimization and applications Vol. 60; no. 2; pp. 393 - 411 |
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| Format: | Journal Article |
| Language: | English |
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Boston
Springer US
01.03.2015
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
| Online Access: | Get full text |
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| Abstract | Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical method for the determination of optimal scenarios is presented. A new derivative-free descent method for the solution of set optimization problems is given together with numerical results in low dimensions. |
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| AbstractList | Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical method for the determination of optimal scenarios is presented. A new derivative-free descent method for the solution of set optimization problems is given together with numerical results in low dimensions. |
| Author | Jahn, Johannes |
| Author_xml | – sequence: 1 givenname: Johannes surname: Jahn fullname: Jahn, Johannes email: johannes.jahn@fau.de organization: Department Mathematik, Universität Erlangen-Nürnberg |
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| CitedBy_id | crossref_primary_10_1007_s10957_021_01887_y crossref_primary_10_1007_s11117_024_01089_6 crossref_primary_10_1007_s10957_025_02772_8 crossref_primary_10_1007_s00186_016_0541_5 crossref_primary_10_1137_21M143683X crossref_primary_10_1007_s10957_016_0993_z crossref_primary_10_1080_0305215X_2024_2433077 crossref_primary_10_1080_02331934_2024_2390116 crossref_primary_10_1007_s10013_017_0263_x crossref_primary_10_1007_s10898_017_0518_9 crossref_primary_10_1080_02331934_2017_1310211 crossref_primary_10_1080_02331934_2021_1988596 crossref_primary_10_1007_s10898_019_00815_9 crossref_primary_10_1080_02331934_2016_1219355 |
| Cites_doi | 10.1007/BF01584336 10.1016/S0362-546X(97)00213-7 10.1080/02331934.2012.749259 10.1137/S1052623493250780 10.1016/j.jmaa.2006.01.033 10.1137/S1052623496303482 10.1007/BF01457934 10.1007/s10957-010-9752-8 10.1137/S1052623400374495 10.1137/S1052623496303470 10.1016/j.na.2011.05.083 10.1093/comjnl/7.4.308 10.1137/080743494 10.1070/RM1977v032n04ABEH001640 10.1007/BF00934564 10.12988/ams.2013.37419 10.11650/tjm.19.2015.4940 10.1007/s10957-013-0363-z 10.1007/s10898-014-0179-x |
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| DOI | 10.1007/s10589-014-9674-8 |
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| Keywords | 90C29 Set less order relation 06A06 Vectorization 90C56 Set optimization |
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| SubjectTerms | Analysis Computation Computational geometry Computer science Computer simulation Convex and Discrete Geometry Descent Management Science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Numerical analysis Operations Research Operations Research/Decision Theory Optimization Set theory Statistics Studies Vector processing (computers) |
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| Title | A derivative-free descent method in set optimization |
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