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• W2892075628 abstract "This paper is concerned with an uncertain multiobjective optimization problem, where the objective and constraint functions are sums-of-squares--convex (SOS-convex) polynomials, and the uncertainty sets are spectrahedra. Using a robust optimization approach, we first establish necessary and sufficient optimality conditions for weakly efficiencies of the corresponding robust multiobjective optimization problem. These optimality criteria are expressed in terms of sums-of-squares conditions and linear matrix inequalities, which provide a numerically checkable certificate of the solvability of the given optimality conditions. We then propose a dual multiobjective problem by means of sums-of-squares and linear matrix inequalities to the robust multiobjective SOS-convex polynomial optimization problem and examine weak, strong, and converse duality relations between them. In addition, we consider a semidefinite linear programming (SDP) weighted-sum relaxation problem for verifying weighted-sum efficient values of the primal problem." @default.
• W2892075628 created "2018-09-27" @default.
• W2892075628 creator A5024668916 @default.
• W2892075628 date "2018-01-01" @default.
• W2892075628 modified "2023-10-02" @default.
• W2892075628 title "Linear Matrix Inequality Conditions and Duality for a Class of Robust Multiobjective Convex Polynomial Programs" @default.
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• W2892075628 doi "https://doi.org/10.1137/17m1143484" @default.
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