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arXiv · 2312.01428

Approximate Proper Efficiency in Vector Optimization via Benson's Approach

Nguyen Thi Thu Huong
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Abstract

We present two criteria for checking approximate proper efficiency in vector optimization problems with the ordering cone being a nonnegative orthant. Although the criteria can be established by Benson's approach [H.P. Benson, \textit{An improved definition of proper efficiency for vector maximization with respect to cones}, J. Math. Anal. Appl. \textbf{71} (1979), 232--241], detailed proofs are given for the first time here. The two criteria are strong motivations to introduce the concept of $e$-properly efficient solution, where $e$ is any nonzero vector taken from the closed pointed convex ordering cone. For an arbitrary linear vector optimization problem, we show that either the $e$-properly efficient solution set is empty or it coincides with the $e$-efficient solution set. This new result has no analogue in the literature.

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Nguyen Thi Thu Huong. 2023-12-03. Approximate Proper Efficiency in Vector Optimization via Benson's Approach. https://arxiv.org/abs/2312.01428

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