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,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton me...In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton method for solving nonlinear complementarity problems,where a non-monotone line search scheme is used.In particular,we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions.We test the proposed method by solving the test problems from MCPLIB.Numerical experiments indicate that this algorithm has better numerical performance in the case of p=5 andθ∈[0.25,075]than other cases.展开更多
提出一种求解最优潮流(OPF)问题的新算法——解耦半光滑牛顿型算法.该算法是对作者的投影半光滑N ew ton算法的改进和提高,它除了保持原算法不必识别不等式约束、对界约束的特殊处理以减少讨论问题的维数等优点外,其显著的特点是结合了...提出一种求解最优潮流(OPF)问题的新算法——解耦半光滑牛顿型算法.该算法是对作者的投影半光滑N ew ton算法的改进和提高,它除了保持原算法不必识别不等式约束、对界约束的特殊处理以减少讨论问题的维数等优点外,其显著的特点是结合了电力系统固有的弱耦合性质,构造了求解OPF问题的一类解耦半光滑牛顿算法.解耦算法可达到加快计算速度、提高计算效率的目的.IEEE多个算例的数值实验以及与其他方法的比较均显示了新算法具有良好的计算效果.展开更多
Di Pillo和Grippo提出的含参数C＞O的增广Lagrangian函数中,使用了最大函数,该函数可能在无穷多个点处不可微．为了克服这个问题,濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等...Di Pillo和Grippo提出的含参数C＞O的增广Lagrangian函数中,使用了最大函数,该函数可能在无穷多个点处不可微．为了克服这个问题,濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性,且在适当假设下,具有超线性收敛率．但是在该方法中,要求参数C充分大．为了实现算法及提高算法效率,本文给出了一个有效选择参数C的方法．展开更多
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.
文摘In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton method for solving nonlinear complementarity problems,where a non-monotone line search scheme is used.In particular,we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions.We test the proposed method by solving the test problems from MCPLIB.Numerical experiments indicate that this algorithm has better numerical performance in the case of p=5 andθ∈[0.25,075]than other cases.
基金This research is supported by the National Science Foundation of China (No. 10571137) and the Natural Science Foundation of Shanghai Educational Committee(No.05LZ05)
文摘提出一种求解最优潮流(OPF)问题的新算法——解耦半光滑牛顿型算法.该算法是对作者的投影半光滑N ew ton算法的改进和提高,它除了保持原算法不必识别不等式约束、对界约束的特殊处理以减少讨论问题的维数等优点外,其显著的特点是结合了电力系统固有的弱耦合性质,构造了求解OPF问题的一类解耦半光滑牛顿算法.解耦算法可达到加快计算速度、提高计算效率的目的.IEEE多个算例的数值实验以及与其他方法的比较均显示了新算法具有良好的计算效果.
