An approach to characterizing $$\epsilon $$ ϵ -solution sets of convex programs

N. V. Tuyen (), C.-F. Wen () and T. Q. Son ()
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N. V. Tuyen: Hanoi Pedagogical University 2, Xuan Hoa
C.-F. Wen: Kaohsiung Medical University
T. Q. Son: Saigon University, HCMC

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 30, issue 2, No 2, 249-269

Abstract: Abstract In this paper, we propose an approach to characterizing $${\epsilon} $$ ϵ -solution sets of convex programs with a given $${\epsilon} >0$$ ϵ > 0 . The results are divided into two parts. The first one is devoted to establishing the expressions of $${\epsilon} $$ ϵ -solution sets of a class of convex infinite programs. The representation is given based on the study of relationships among the following three sets: the set of Lagrange multipliers corresponding to a given $${\epsilon} $$ ϵ -solution, the set of $${\epsilon} $$ ϵ -solutions of the dual problem corresponding, and the set of $${\epsilon} $$ ϵ -Kuhn–Tucker vectors associated with the problem in consideration. The second one is devoted to some special cases: the $${\epsilon} $$ ϵ -solution sets of convex programs that have set constraints and the almost $${\epsilon} $$ ϵ -solution sets of convex programs that have finite convex constraints. Several examples are given.

Keywords: $${\epsilon} $$ ϵ -solution; $${\epsilon} $$ ϵ -solution set; Minimizing sequence; $${\epsilon} $$ ϵ -Kuhn–Tucker vector; 90C25; 90C34; 90C46; 90C59 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11750-021-00616-y

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