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<p>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, <CitationRef CitationID="CR1">2022</CitationRef>), 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.</p>

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Perturbational Approach to Duality in Evenly Convex Set-Valued Optimization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月13日

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  • María Dolores Fajardo

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.