In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints.This algorithm is based on a tru...A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints.This algorithm is based on a trust region algorithm for nonsmooth unconstrained optimization problems,and its global convergence is also proved.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
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
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
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
The image restoration problems play an important role in remote sensing and astronomical image analysis.One common method for the recovery of a true image from corrupted or blurred image is the least squares error(LSE...The image restoration problems play an important role in remote sensing and astronomical image analysis.One common method for the recovery of a true image from corrupted or blurred image is the least squares error(LSE)method.But the LSE method is unstable in practical applications.A popular way to overcome instability is the Tikhonov regularization.However,difficulties will encounter when adjusting the so-called regularization parameter a.Moreover,how to truncate the iteration at appropriate steps is also challenging.In this paper we use the trust region method to deal with the image restoration problem,meanwhile,the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method.We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded.The trust region method is very stable and robust,and it has the nice property of updating the trust region automatically.This releases us from tedious finding the regularization parameters and truncation levels.Some numerical tests on remotely sensed images are given to show that the trust region method is promising.展开更多
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...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
摘要In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
基金supported by the National Natural Science Foundation of China(Grant No.19731001)the Management.Decison and Infomation System Lab,Chinese Academy of Sciences.
摘要A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints.This algorithm is based on a trust region algorithm for nonsmooth unconstrained optimization problems,and its global convergence is also proved.
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
摘要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.
基金Supported by the National Natural Science Foundation of China(No.11171348,11171252 and 71232011)
摘要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.
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
摘要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.
摘要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supported by the National Natural Science Foundation of China(Grant Nos.19731010 and 10231060)the Knowledge Innovation Program of CAS+1 种基金was supported by SRF for ROSS,SEMpartially supported by the Special Innovation Fund for graduate students of CAS.
摘要The image restoration problems play an important role in remote sensing and astronomical image analysis.One common method for the recovery of a true image from corrupted or blurred image is the least squares error(LSE)method.But the LSE method is unstable in practical applications.A popular way to overcome instability is the Tikhonov regularization.However,difficulties will encounter when adjusting the so-called regularization parameter a.Moreover,how to truncate the iteration at appropriate steps is also challenging.In this paper we use the trust region method to deal with the image restoration problem,meanwhile,the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method.We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded.The trust region method is very stable and robust,and it has the nice property of updating the trust region automatically.This releases us from tedious finding the regularization parameters and truncation levels.Some numerical tests on remotely sensed images are given to show that the trust region method is promising.
基金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)
摘要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.