Optimization Online


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


Download: [PDF]

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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society