Stability of minimizers of set optimization problems
Sign Up to like & getrecommendations! Published in 2017 at "Positivity"
DOI: 10.1007/s11117-016-0412-6
Abstract: We study the asymptotic behavior of sequences of minimization problems in set optimization. More precisely, considering a sequence of set optimization problems $$(P_n)$$(Pn) converging in some sense to a set optimization problem (P) we investigate the upper… read more here.
Keywords: optimization; minimizers set; optimization problems; set optimization ... See more keywords
On Levitin–Polyak well-posedness and stability in set optimization
Sign Up to like & getrecommendations! Published in 2021 at "Positivity"
DOI: 10.1007/s11117-021-00849-y
Abstract: In this paper, Levitin–Polyak (in short LP) well-posedness in the set and scalar sense are defined for a set optimization problem and a relationship between them is found. Necessary and sufficiency criteria for the LP… read more here.
Keywords: set optimization; well posedness; levitin polyak;
Solving set optimization problems based on the concept of null set
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.12.021
Abstract: Abstract We introduce the concept of null set in the hyperspace that is consisting of all nonempty subsets of a given normed space. Based on the concepts of null set and convex cone, we can… read more here.
Keywords: optimization; null set; problem; concept null ... See more keywords
Set optimization by means of variable order relations
Sign Up to like & getrecommendations! Published in 2017 at "Optimization"
DOI: 10.1080/02331934.2016.1172226
Abstract: We introduce several variable order relations to compare sets in a linear topological space and we consider set optimization problems equipped with these variable ordering structures. By considering a set approach, we introduce characterizations for… read more here.
Keywords: order relations; optimization means; optimization; variable order ... See more keywords
Scalarization of Levitin–Polyak well-posed set optimization problems
Sign Up to like & getrecommendations! Published in 2017 at "Optimization"
DOI: 10.1080/02331934.2016.1253086
Abstract: Abstract The aim of this paper is to study Levitin–Polyak (LP in short) well-posedness for set optimization problems. We define the global notions of metrically well-setness and metrically LP well-setness and the pointwise notions of… read more here.
Keywords: levitin polyak; well posedness; metrically well; optimization ... See more keywords
Six set scalarizations based on the oriented distance: properties and application to set optimization
Sign Up to like & getrecommendations! Published in 2019 at "Optimization"
DOI: 10.1080/02331934.2019.1598406
Abstract: ABSTRACT In the framework of normed spaces ordered by a convex cone not necessarily solid, we present six set scalarization functions which are extensions of the oriented distance of Hiriart-Urruty. We investigate their relationships and… read more here.
Keywords: set optimization; six set; optimization; oriented distance ... See more keywords
Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets
Sign Up to like & getrecommendations! Published in 2019 at "Optimization"
DOI: 10.1080/02331934.2020.1812605
Abstract: Set-optimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set-valued objective function. Ther... read more here.
Keywords: optimality conditions; optimization using; using directional; optimization ... See more keywords