In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal compone...In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal component being separated from computation 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. Because 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 opthnization. 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.展开更多
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
基金Supported by the National Natural Sciences Foundation of China (No.39830070 and 10171055).
文摘In this paper, a new SQP method for inequality constrained optimization is proposed and the global convergence is obtained under very mild conditions.
基金This research is supported in part by the National Natural Science Foundation of China(Grant No. 39830070,10171055)and China Postdoctoral Science Foundation
文摘In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal component being separated from computation 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. Because 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 opthnization. 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.
基金This research is supported in part by the National Natural Science Foundation of China(No. 39830070).
文摘In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
