High performance grid and cluster computing for some optimization problems

The aim of this short article is to show that grid and cluster computing provides tremendous power to optimization methods. The methods that the article picks up are a successive convex relaxation method for quadratic optimization problems, a polyhedral homotopy method for polynomial systems of equations and a primal-dual interior-point method for semidefinite programming problems. Their parallel implementations on grids and clusters together with numerical results are reported.