论文信息 - An explicit construction of distinguished representations of polynomials nonnegative over finite sets

An explicit construction of distinguished representations of polynomials nonnegative over finite sets

We present a simple constructive proof of the existence of distinguished sum of squares representations for polynomials nonnegative over finite sets described by polynomial equalities and inequalities. A degree bound is directly obtained, as the cardinality of the support of the summands equals the number of points in the variety. Only basic results from commutative algebra are used in the construction.

P. Parrilo

[1] N. Z. Shor. Class of global minimum bounds of polynomial functions , 1987 .

[2] Donal O'Shea,et al. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[3] Yurii Nesterov,et al. Squared Functional Systems and Optimization Problems , 2000 .

[4] P. Parrilo. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[5] Charles N. Delzell,et al. Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra , 2001 .

[6] A. Prestel,et al. Distinguished representations of strictly positive polynomials , 2001 .

[7] Jean B. Lasserre,et al. Polynomials nonnegative on a grid and discrete optimization , 2001 .

[8] Jean B. Lasserre,et al. Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[9] Pablo A. Parrilo,et al. Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..