Abstract cones of positive polynomials and their sums of squares relaxations
نویسنده
چکیده
cones of positive polynomials and their sums of squares relaxations
منابع مشابه
An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones
This paper is based on a recent work by Kojima which extended sums of squares relaxations of polynomial optimization problems to polynomial semidefinite programs. Let E and E+ be a finite dimensional real vector space and a symmetric cone embedded in E ; examples of E and E+ include a pair of the N -dimensional Euclidean space and its nonnegative orthant, a pair of the N -dimensional Euclidean ...
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We consider the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities, which is NP-hard in general. Hierarchies of semidefinite relaxations have been proposed in the literature, involving positive semidefinite moment matrices and the dual theory of sums of squares of polynomials. We present these hierarchies of approximations and their main...
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Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP usin...
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تاریخ انتشار 2010