Constrained nonlinear optimization problems widely exist in mechanical analysis and deigns problems. Some of them are very difficult to be solved, and there is no absolutely reliable method to locate the global optima of these problems. In this paper, a new approach is investigated which is more efficient than some existing methods. As is well known, constrained variable metric algorithm possesses a rapid convergence speed and strong ability to locate local optima. However, its ability to locate global optima need to be improved. On the other hand, the chaotic optimization algorithm, which uses the ergodicity, stochastic and regularity of chaotic motion, possesses strong ability to jump out local minima and rather weaker ability to locate local minimum finely. By combining the chaotic optimization algorithm and constrained variable metric algorithm, a new method, which is named as chaotic variable metric method, is proposed to solve constrained nonlinear optimization problems. In the proposed method, the chaotic optimization algorithm serves to help the constrained variable metric algorithm to jump out local minima and the constrained variable metric algorithm serves to improve the ability of the chaotic optimization algorithm to locate local minima. The presented method gives attention to both the advantages of the chaotic optimization algorithm and those of the constrained variable metric algorithm. Numerical results show that the present method is efficient in solving constrained nonlinear optimization problems.
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