Conjugate Duality in Constrained Set-Valued Vector Optimization Problems

Li, S. J.; Sun, Xiang-Kai; Liu, H. M.; Yao, S. F.; Teo, Kok Lay

doi:10.1080/01630563.2010.528567

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Comments On Set Optimization Duality1

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Cited by 3 publications

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“…Assumptions, of course, include int C = ∅. The same assumption also is crucial in [124]; Theorem 3.2 and 3.3 therein is probably as far as one get in terms of conjugate duality based on "suprema" of a set, i.e. the elements which belong to the closure of the set, but are not dominated with respect to the relation which is generated by the interior of the ordering cone.…”

Section: Comments On Set Optimization Dualitymentioning

confidence: 99%

Set Optimization—A Rather Short Introduction

Hamel

Heyde

Löhne

et al. 2015

Springer Proceedings in Mathematics &Amp; Statistics

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Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for setand vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems.

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Section: Comments On Set Optimization Dualitymentioning

confidence: 99%