Ju Liang ZHANG;Xiang Sun ZHANG;Xin Jian ZHUO
Journal of Systems Science and Complexity. 2003, 16(4): 494-505.
In this paper, a trust region method for equality constrained optimization . based on nondifferentiable exact penalty is proposed. In this algorithm, the trail step is characterized by computation of its normal component being separated from compu-tation of its tangential component, i.e., only the tangential component of the trail step is constrained by trust radius while the normal component and trail step itself have no constraints. The other main characteristic of the algorithm is the decision of trust region radius. Here, the decision of trust region radius uses the information of the gradient of objective function and reduced Hessian. However, Maratos effect will occur when we use the nondifferentiable exact penalty function as the merit function. In order to obtain the superlinear convergence of the algorithm, we use the twice order correction technique. Be-cause of the speciality of the adaptive trust region method, we use twice order correction when p = 0 (the definition is as in Section 2) and this is different from the traditional trust region methods for equality constrained optimization. So the computation of the algorithm in this paper is reduced. What is more, we can prove that the algorithm is globally and superlinearly convergent.
