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
This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the gl...This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.展开更多
In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component ...In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced Hessian.However, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent.展开更多
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
This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than ...This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.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
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.
文摘This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
基金This research is supported in part by the National Natural Science Foundation of China(Grant No. 39830070,10171055)and China Postdoctoral Science Foundation
文摘In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced Hessian.However, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent.
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.
基金This research is partly supported by the Hunan Provincial Natural Science Foundtion of China and Hunan Provincial Education Foundation of China 02B021
文摘This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.
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
