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In this study, we propose a new constrained optimization method using the quasi-chaotic optimization method (Q-COM) with the exact penalty function and the Sequential Quadratic Programming (SQP). The Q-COM, which has been proposed recently, is a global optimization method to solve unconstrained optimization problems in which the simultaneous perturbation gradient approximation is introduced into the chaotic optimization method to apply to a class of problems whose objective function values only can be computed. The SQP is well known and powerful constrained optimization method to find local optimal solution. In the proposed method, the Q-COM with the exact penalty function is used as the global search method and the SQP is used as the local search method. We confirm the effectiveness of the proposed method through applications to various types of benchmark problems that include the coil spring design problem and the benchmark problems used in the special session on constrained real parameter optimization in CEC2006.