In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalit...In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.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
The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies...The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.展开更多
基金supported by Guangdong Provincial Zhujiang Scholar Award Project,National Science Foundation of China(10671163,10871031)the National Basic Research Program under the Grant 2005CB321703Scientific Research Fund of Hunan Provincial Education Department(06A069,06C824)
文摘In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.
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.
文摘The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.
