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Variational principles in set optimization with domination structures and application to changing jobs

Abstract : This paper is devoted to new versions of Ekeland’s variational principle in set optimization with domination structure, where set optimization is an extension of vector optimization from vector-valued functions to set-valued maps using Kuroiwa’s set-less relations to compare one entire image set with another whole image set, and where domination structure is an extension of ordering cone in vector optimization; it assigns each element of the image space to its own domination set. We use Gerstewitz’s nonlinear scalarization function to convert a set-valued map into an extended real-valued function and the idea of the proof of Dancs-Hegedüs-Medvegyev’s fixed-point theorem. Our setting is applicable to dynamic processes of changing jobs in which the cost function does not satisfy the symmetry axiom of metrics and the class of set-valued maps acting from a quasimetric space into a real linear space. The obtained result is new even in simpler settings.
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Submitted on : Tuesday, March 3, 2020 - 2:24:50 PM
Last modification on : Wednesday, August 5, 2020 - 3:13:05 AM

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Truong Quang Bao, Antoine Soubeyran. Variational principles in set optimization with domination structures and application to changing jobs. Journal of Applied and Numerical Optimization, 2019, 1 (3), pp.217-241. ⟨10.23952/jano.1.2019.3.03⟩. ⟨hal-02497051⟩

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