We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to...

We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity....

Recently, given the first few moments, tight upper and lower bounds of the no arbitrage prices can be obtained by solving semidefinite programming (SDP) or linear programming (LP) problems. In this paper, we compare SDP and LP formulations of the European-style options pricing problem and prefer...