Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization

Thai Doan Chuong ()
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Thai Doan Chuong: Ton Duc Thang University

Annals of Operations Research, 2022, vol. 311, issue 2, No 18, 997-1015

Abstract: Abstract In this paper, we employ some advanced tools of variational analysis to provide new necessary optimality conditions for approximate (weak) Pareto solutions of a nonconvex and nonsmooth cone constrained vector optimization problem. The obtained necessary conditions are exhibited in a fuzzy form and a Fritz-John type. Sufficient optimality conditions for approximate (weak) Pareto solutions of the multiobjective problem are established by using assumptions of (strictly) approximately generalized convexity. Moreover, we address an approximate dual vector problem for the cone constrained vector optimization problem and examine converse and strong dualities for approximate (weak) Pareto solutions.

Keywords: Approximate vector optimization; Optimality conditions; Cone constrained; Dual problem; Subdifferential; 49K99; 90C46; 90C29; 65K10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-020-03740-3

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