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A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality

Gemayqzel Bouza(gema***at***matcom.uh.cu)
Ernest Quintana(ernest.quintana***at***tu-ilmenau.de)
Christiane Tammer(christiane.tammer***at***mathematik.uni-halle.de)

Abstract: In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent to finding optimistic solutions to vector optimization problems under uncertainty with a finite uncertainty set. We develop optimality conditions for these types of problems, and introduce two concepts of critical points. Furthermore, we propose a descent method and provide a convergence result to points satisfying the optimality conditions previously derived. Some numerical examples illustrating the performance of the method are also discussed. This paper is a modified and polished version of Chapter 5 in the dissertation by Quintana [43].

Keywords: set optimization, robust vector optimization, descent method, stationary point

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Robust Optimization

Citation:

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Entry Submitted: 01/15/2021
Entry Accepted: 01/15/2021
Entry Last Modified: 01/15/2021

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