A trust region algorithm for equality constrained optimization is proposed, which is a nonmonotone one in a certain sense. The augmented Lagrangian function is used as a merit function. Under certain conditions, the g...A trust region algorithm for equality constrained optimization is proposed, which is a nonmonotone one in a certain sense. The augmented Lagrangian function is used as a merit function. Under certain conditions, the global convergence theorems of the algorithm are proved.展开更多
A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing tr...A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed.展开更多
In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region al...In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model展开更多
Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization prob...Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.展开更多
In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization pro...In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization problem (COP), a class of nonmonotone trust region algorithmsis proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms isproved. In sec. 3, some results about the Cauchy point are provided. The展开更多
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
基金Project supported by the National Natural Science Foundation of China and Postdoctoral Foundation of China.
文摘A trust region algorithm for equality constrained optimization is proposed, which is a nonmonotone one in a certain sense. The augmented Lagrangian function is used as a merit function. Under certain conditions, the global convergence theorems of the algorithm are proved.
文摘A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the global and Q quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii are also discussed.
文摘In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model
文摘Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.
基金Project supported by the National Natural Science Foundation of China and Postdoctoral Foundation of China.
文摘In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization problem (COP), a class of nonmonotone trust region algorithmsis proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms isproved. In sec. 3, some results about the Cauchy point are provided. The
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The National Natural Science Foundation of China (10231060)the Special Research Fund of Doctoral Program of Higher Education of China (20040319003)the Graduates' Creative Project of Jiangsu Province,China.
