In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorith...In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.展开更多
A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm i...A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.展开更多
Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented...Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.展开更多
In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming proble...In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.展开更多
We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust regi...We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.展开更多
Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N...Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; Numerical results of the study.展开更多
基金Supported by CERG: CityU 101005 of the Government of Hong Kong SAR, Chinathe National Natural ScienceFoundation of China, the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No.20040319003)the Natural Science Fund of Jiangsu Province of China (Grant No. BK2006214)
文摘In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.
文摘A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.
基金Research partially supported by the Faculty Research Grant RIG-35547 and ROG-34628 of the University of North Texas and in part by the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation with ad
文摘Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(No.11171348,11171252 and 71232011)
文摘In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.
文摘We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algo- rithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.
基金Chinese NSF grants 19525101, 19731001, and by State key project 96-221-04-02-02. It is also partially supported by Hebei provi
文摘Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; Numerical results of the study.
