Solving large scale optimization problems requires a huge amount of computational power. The size of optimization problems that can be solved on a few CPUs has been limited due to a lack of computational power. Grid and cluster computing has received much attention as a powerful and inexpensive way of solving large scale optimization problems that an existing single-unit CPU cannot process. The aim of this paper is to show that grid and cluster computing provides tremendous power to optimization methods. The methods that this paper 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 interiorpoint method for semidefinite programs. Their parallel implementations on grids and clusters together with numerical results are reported. The paper also mentions a grid portal system for optimization problems briefly.