Constrained Optimization using the Lagrangian Method and the Improved Discrete Gradient Chaos Model

In this study, we propose a new chaotic global optimization method using the Lagrangian method to solve a nonlinear constrained optimization problem. Firstly, we explain the convergence behavior of the first order method regarding convexity of the Lagrangian with respect to decision variables in terms of linear stability theory. Further, we propose a new optimization method in which the convergence behavior of the first order method is improved by two techniques. One is the introduction of a coupling structure. The second is the introduction of objective function weighting. Then, we apply a multipoint type chaotic optimization method so that global search is implemented to find feasible global minima. We then confirm the effectiveness of the proposed method through applications to the coil spring design problem and benchmark problems used in the special session on constrained real parameter optimization in CEC2006.