Necessary Conditions for Nondominated Solutions in Vector Optimization

Truong Q. Bao (), Lidia Huerga (), Bienvenido Jiménez () and Vicente Novo ()
Additional contact information
Truong Q. Bao: Northern Michigan University
Lidia Huerga: UNED
Bienvenido Jiménez: UNED
Vicente Novo: UNED

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 5, 826-842

Abstract: Abstract In this paper, we study characterizations and necessary conditions for nondominated points of sets and nondominated solutions of vector-valued functions in vector optimization with variable domination structure. We study not only the case, where the intersection of all the involved domination sets has a nonzero element, but also the case, where it might be the singleton. While the first case has been studied earlier, the second case has not, to the best of our knowledge, done yet. Our results extend and improve the existing results in vector optimization with a fixed ordering cone and with a variable ordering structure.

Keywords: Vector optimization; Domination structures; Nondominated solutions; Generalized differentiation; Nonlinear scalarization functions; 49J52; 49J53; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01732-8

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