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.
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Chuong, T.D. Second-order cone programming relaxations for a class of multiobjective convex polynomial problems. Ann Oper Res 311, 1017–1033 (2022). https://doi.org/10.1007/s10479-020-03577-w
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DOI: https://doi.org/10.1007/s10479-020-03577-w
Keywords
- Multiobjective optimization
- Duality
- 1st-SDSOS-convex polynomial
- Second-order cone condition
- Slater condition