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- W1993400404 abstract "In this paper we introduce a new dual program, which is representable as a semi-definite linear programming problem, for a primal convex minimax programming model problem and show that there is no duality gap between the primal and the dual whenever the functions involved are SOS-convex polynomials. Under a suitable constraint qualification, we derive strong duality results for this class of minimax problems. Consequently, we present applications of our results to robust SOS-convex programming problems under data uncertainty and to minimax fractional programming problems with SOS-convex polynomials. We obtain these results by first establishing sum of squares polynomial representations of non-negativity of a convex max function over a system of SOS-convex constraints. The new class of SOS-convex polynomials is an important subclass of convex polynomials and it includes convex quadratic functions and separable convex polynomials. The SOS-convexity of polynomials can numerically be checked by solving semi-definite programming problems whereas numerically verifying convexity of polynomials is generally very hard." @default.
- W1993400404 created "2016-06-24" @default.
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- W1993400404 date "2013-12-05" @default.
- W1993400404 modified "2023-09-27" @default.
- W1993400404 title "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs" @default.
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- W1993400404 doi "https://doi.org/10.1007/s10957-013-0496-0" @default.
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