A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by t...In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing FisheroBurmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. ~rthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.展开更多
In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction...In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.展开更多
A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possibl...A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.展开更多
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new...This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.展开更多
In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatu...In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.展开更多
This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is mon...This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.展开更多
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
基金Supported-by the National Natural Science Foundation of China(10371089)and the Foundation of Qingdao University
文摘In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing FisheroBurmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. ~rthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.
基金Supported by National Natural Science Foundation of China (Grant Nos. 11061011 and 71061002)Guangxi Fund for Distinguished Young Scholars (2012GXSFFA060003)
文摘In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.
基金This research is supportedin part by the National Natural Science Foundation ofChina(Grant No. 39830070).
文摘A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.
基金the Scientific Research Foundation of Hunan Provincial Education Department, No. 02B021, and the National Natural Science Foundation of China, No. 10171008.
文摘This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
文摘In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.
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.
文摘This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.
