Complexity Analyses of Discretized Successive Convex Relaxation Methods

We investigate the computational complexity of discretized successive convex relaxation methods in the way of upper bounding the number of major iterations required, in the worst case. Kojima and Takeda [2] earlier analyzed the computational complexity of semi-in nite successive convex relaxation methods (these methods require the solution of in nitely many linear programming or semide nite programming problems with in nitely many constraints to be solved during each major iteration). Our analyses extend Kojima-Takeda analysis to the discretized successive convex relaxation methods which require the solution of nitely many ordinary linear programming or semide nite programming problems in each major iteration. Our complexity bounds are within a small constant (four) multiple of theirs.