Convex Relaxation for Solving Polynomial Programs through Quadratization Technique

Abstract

In this paper, we study convex quadratic relaxation in polynomial programming. The goal is to solve polynomial programs through quadratic reformulation with the factorization method. The quadratization of monomials of degree more than two is carried out by replacing each pair of factors of the monomial with auxiliary variables. In this paper, each pair of factors of a monomial will be considered. The quadratic program obtained is convexified by using eigenvalues. As a result, the quadratic reformulation involving all factors of the monomial strengthens the information of the polynomial function but increases the dimensionality of the variables significantly. The next work is to develop a strategy to reduce the dimensions of the auxiliary variables.