Second-order cone programming relaxations for a class of multiobjective convex polynomial problems

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

Annals of Operations Research, 2022, vol. 311, issue 2, No 19, 1017-1033

Abstract: Abstract This paper is concerned with a multiobjective convex polynomial problem, where the objective and constraint functions are first-order scaled diagonally dominant sums-of-squares convex polynomials. We first establish necessary and sufficient optimality criteria in terms of second-order cone (SOC) conditions for (weak) efficiencies of the underlying multiobjective optimization problem. We then show that the obtained result provides us a way to find (weak) efficient solutions of the multiobjective program by solving a scalar second-order cone programming relaxation problem of a given weighted-sum optimization problem. In addition, we propose a dual multiobjective problem by means of SOC conditions to the multiobjective optimization problem and examine weak, strong and converse duality relations.

Keywords: Multiobjective optimization; Duality; 1st-SDSOS-convex polynomial; Second-order cone condition; Slater condition; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-020-03577-w

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