This paper describes an optimizing algorithm for a global optimization problem, which has multi-local optimum solutions. 0n structural optimizations, some problems cannot be solved by using nonlinear programming method for convex optimization problem, because those are non-convex problem by complexity of constraint or objective function itself. Therefore, the global optimizing system that makes use of local optimizing procedure is needed for more effective searching in some design problems. The proposed method is to be characterized by using clustering procedure for convex subspaces, which are formed in a local optimizing procedure, and by using Lebesque measurement to evaluate a termination criterion. In order to evaluate the effectiveness of the algorithm, some numerical examples are illustrated