Record Details

On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances

Digitale Bibliothek Thüringen

View Archive Info
 
 
Field Value
 
Title On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances
 
Creator Eichfelder, Gabriele
Gerlach, Tobias
 
Type article
Text
doc-type:article
 
Identifier http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200588
https://www.db-thueringen.de/receive/dbt_mods_00034052
https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00040238/IfM_Preprint_M_18_01.pdf
http://uri.gbv.de/document/gvk:ppn:1011918099
 
Subject article
ddc:510
Order relations -- Set optimization -- Set approach -- Test instances -- Vector optimization
 
Description 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.
 
Date 2018-01-29
 
Format 25 Seiten
 
Language eng
 
Rights public
all rights reserved
info:eu-repo/semantics/openAccess