Perturbational Approach to Duality in Evenly Convex Set-Valued Optimization

被引：0

作者：

María Dolores Fajardo ^{[1
]}

机构：

[1] University of Alicante,Department of Mathematics

来源：

Set-Valued and Variational Analysis | 2025年 / 33卷 / 2期

关键词：

Set-valued optimization; Evenly convex sets; Convex duality theory; Convex conjugation; Complete lattice; Strong duality; 49N15; 52A07; 90C46; 90C48;

D O I：

10.1007/s11228-025-00756-4

中图分类号：

学科分类号：

摘要：

A general perturbation approach to conjugate duality theory in set-valued optimization considering set criterion, where the image space is a complete lattice whose elements are evenly convex sets, is presented. This image space structure is suitable for the conjugation scheme for set-valued functions which was defined in a previous work (Fajardo in Set-Valued Var. Anal. 30:827-846, 2022), and it allows to obtain a dual problem for a general primal one verifying weak dualty. Fenchel and Lagrange dual problems are presented as examples. We also obtain zero duality gap and strong duality theorems.

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