Details:
Title  Semidefinite representations for finite varieties  Author(s)  Monique Laurent  Type  Technical Report, Misc  Abstract  We consider the problem of minimizing a polynomial over a set defined by polynomial equations and inequalities. When the polynomial equations have a finite set of complex solutions, we can reformulate this problem as a semidefinite programming problem. Our semidefinite representation involves combinatorial moment matrices, which are matrices indexed by a basis of the quotient vector space R[x_1, ..., x_n]/I, where I is the ideal generated by the polynomial equations in the problem. Moreover, we prove the finite convergence of a hierarchy of semidefinite relaxations introduced by Lasserre. Semidefinite approximations can be constructed by considering truncated combinatorial moment matrices; rank conditions are given (in a grid case) that ensure that the approximation solves the original problem to optimality. 
URL 
http://homepages.cwi.nl/~monique/ 
Language  English  Year  2004  Month  June  Edition  0  Translation 
No  Refereed 
No 
