The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we ...The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.展开更多
This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with...This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the pro- posed algorithm.展开更多
We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where th...We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.展开更多
In this paper,we propose a new nonmonotone trust region Barzilai-Borwein(BB for short)method for solving unconstrained optimization problems.The proposed method is given by a novel combination of a modified Metropolis...In this paper,we propose a new nonmonotone trust region Barzilai-Borwein(BB for short)method for solving unconstrained optimization problems.The proposed method is given by a novel combination of a modified Metropolis criterion,BB-stepsize and trust region method.The new method uses the reciprocal of BB-stepsize to approximate the Hessian matrix of the objective function in the trust region subproblems,and accepts some bad solutions according to the modified Metropolis criterion based on simulated annealing idea.Under some suitable assumptions,the global convergence of the new method is established.Some preliminary numerical results indicate that,the new method is more efficient compared with the existing trust region BB method.展开更多
Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which ...Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.展开更多
In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gra...In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gradient and Lanczos methods.Using the backtracking line search,we will find an acceptable trial step size along this direction which makes the objective function nonmonotonically decreasing and makes the norm of the step size monotonically increasing.Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions.Finally,we present some numerical results to illustrate the effectiveness of the proposed algorithm.展开更多
In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumul...In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumulation points of the iterates generated by the proposed algorithm are Kuhn-Tucker points and that the algorithm is q-superlinearly convergent.展开更多
In this paper,we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems.More precisely,a trust-region radius based on a nonmonotone technique uses an approximation of Hes...In this paper,we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems.More precisely,a trust-region radius based on a nonmonotone technique uses an approximation of Hessian which is adaptively chosen.We produce a suitable trust-region radius;preserve the global convergence under classical assumptions to the first-order critical points;improve the practical performance of the new algorithm compared to other exiting variants.Moreover,the quadratic convergence rate is established under suitable conditions.Computational results on the CUTEst test collection of unconstrained problems are presented to show the effectiveness of the proposed algorithm compared with some exiting methods.展开更多
We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian...We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.展开更多
文摘The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.
基金Project supported by the National Natural Science Foundation of China (No. 10871130)the Ph. D.Programs Foundation of Ministry of Education of China (No. 20093127110005)the Shanghai Leading Academic Discipline Project (No. T0401)
文摘This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the pro- posed algorithm.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 11171159),the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No. 20103207110002), the Fund for Innovative Program of Jiangsu Province (Grant No. CXLX12_0387), CNPq-Brazil (Grant No. 301748/ 2011-0), and the Research Fund of Pontifical Catholic University of Parana, Brazil.
文摘We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.
基金supported by the National Natural Science Foundation of China(Nos.12071398,11671125,11571074,61977017)the Natural Science Foundation of Hunan Province(No.2020JJ4567)the Key Scientific Research Found of Hunan Education Department(No.20A097)。
文摘In this paper,we propose a new nonmonotone trust region Barzilai-Borwein(BB for short)method for solving unconstrained optimization problems.The proposed method is given by a novel combination of a modified Metropolis criterion,BB-stepsize and trust region method.The new method uses the reciprocal of BB-stepsize to approximate the Hessian matrix of the objective function in the trust region subproblems,and accepts some bad solutions according to the modified Metropolis criterion based on simulated annealing idea.Under some suitable assumptions,the global convergence of the new method is established.Some preliminary numerical results indicate that,the new method is more efficient compared with the existing trust region BB method.
基金the Chinese National Science Foundation Grant 10071050, the Science andTechnology Foundation of Shanghai Higher Education.
文摘Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.
基金supports of the National Natural Science Foundation of China(No.11371253).
文摘In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gradient and Lanczos methods.Using the backtracking line search,we will find an acceptable trial step size along this direction which makes the objective function nonmonotonically decreasing and makes the norm of the step size monotonically increasing.Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions.Finally,we present some numerical results to illustrate the effectiveness of the proposed algorithm.
文摘In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumulation points of the iterates generated by the proposed algorithm are Kuhn-Tucker points and that the algorithm is q-superlinearly convergent.
文摘In this paper,we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems.More precisely,a trust-region radius based on a nonmonotone technique uses an approximation of Hessian which is adaptively chosen.We produce a suitable trust-region radius;preserve the global convergence under classical assumptions to the first-order critical points;improve the practical performance of the new algorithm compared to other exiting variants.Moreover,the quadratic convergence rate is established under suitable conditions.Computational results on the CUTEst test collection of unconstrained problems are presented to show the effectiveness of the proposed algorithm compared with some exiting methods.
基金the National Science Foundation Grant (10871130) of Chinathe Ph.D.Foundation Grant (0527003)+1 种基金the Shanghai Leading Academic Discipline Project (T0401)the Science Foundation Grant (05DZ11) of Shanghai Education Committee
文摘We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.