Robust second order cone conditions and duality for multiobjective problems under uncertainty data

Cao Thanh Tinh () and Thai Doan Chuong ()
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Cao Thanh Tinh: Vietnam National University
Thai Doan Chuong: Brunel University London

Journal of Global Optimization, 2024, vol. 88, issue 4, No 4, 926 pages

Abstract: Abstract This paper studies a class of multiobjective convex polynomial problems, where both the constraint and objective functions involve uncertain parameters that reside in ellipsoidal uncertainty sets. Employing the robust deterministic approach, we provide necessary conditions and sufficient conditions, which are exhibited in relation to second order cone conditions, for robust (weak) Pareto solutions of the uncertain multiobjective optimization problem. A dual multiobjective problem is proposed to examine robust converse, robust weak and robust strong duality relations between the primal and dual problems. Moreover, we establish robust solution relationships between the uncertain multiobjective optimization program and a (scalar) second order cone programming relaxation problem of a corresponding weighted-sum optimization problem. This in particular shows that we can find a robust (weak) Pareto solution of the uncertain multiobjective optimization problem by solving a second order cone programming relaxation.

Keywords: Multiobjective optimization; Second order cone programming; Robust optimization; Convex polynomial; Optimality condition; 65K10; 49K99; 90C46; 90C29 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01335-3

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