000K  utf8
0100  1011918099
1100  2018$c2018-01-29
1500  eng
2050  urn:nbn:de:gbv:ilm1-2017200588
3000  Eichfelder, Gabriele
3010  Gerlach, Tobias
4000  On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances  [Eichfelder, Gabriele]
4060  25 Seiten
4209  Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range of theoretical tools as scalarization approaches and derivative concepts as well as first numerical algorithms are available. These numerical algorithms require on the one hand test instances where the optimal solution sets are known. On the other hand, in most examples and test instances in the literature only set-valued maps with a very simple structure are used. We study in this paper such special set-valued maps and we show that some of them are such simple that they can equivalently be expressed as a vector optimization problem. Thus we try to start drawing a line between simple set-valued problems and such problems which have no representation as multiobjective problems. Those having a representation can be used for defining test instances for numerical algorithms with easy verifiable optimal solution set.
4950  https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2017200588$xR$3Volltext$534
4961  http://uri.gbv.de/document/gvk:ppn:1011918099
5051  510
5550  Order relations
5550  Set approach
5550  Set optimization
5550  Test instances
5550  Vector optimization