Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based p...Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based predictor-corrector integrators are a widely used approach for calculating the trajectories of moving atoms in direct dynamics simulations.We employ a monodromy matrix to propose a tool for evaluating the accuracy of integrators in the trajectory calculation.We choose a general velocity Verlet as a different object.We also simulate molecular with hydrogen(CO_2) and molecular with hydrogen(H_2O) motions.Comparing the eigenvalues of monodromy matrix,many simulations show that Hessian-based predictor-corrector integrators perform well for Hessian updates and non-Hessian updates.Hessian-based predictor-corrector integrator with Hessian update has a strong performance in the H_2O simulations.Hessian-based predictor-corrector integrator with Hessian update has a strong performance when the integrating step of the velocity Verlet approach is tripled for the predicting step.In the CO_2 simulations,a strong performance occurs when the integrating step is a multiple of five.展开更多
It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_＊（κ） linear complementarity problems.This paper presents an extension of t...It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_＊（κ） linear complementarity problems.This paper presents an extension of the recent variant of Mehrotra＇s second order algorithm for linear optimijation.It is shown that the iteration-complexity bound of the algorithm is O（4κ ＋ 3）√14κ ＋ 5 nlog（x0）Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization.展开更多
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In th...Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed.In eac h iteration,the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory.Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required.It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method.Numerical experiments on twenty-six standard test problems are made.The result s show that the proposed algorithm is stable and robust.展开更多
可再生能源的波动性、随机性和需求响应的不确定性对电力系统的静态电压稳定评估带来全新挑战,静态电压稳定域（static voltage stability region,SVSR）是分析和评估含随机性和不确定性因素影响的电力系统电压稳定性的重要工具。传统...可再生能源的波动性、随机性和需求响应的不确定性对电力系统的静态电压稳定评估带来全新挑战,静态电压稳定域（static voltage stability region,SVSR）是分析和评估含随机性和不确定性因素影响的电力系统电压稳定性的重要工具。传统基于连续潮流的SVSR构建方法虽可保证构建精度,但计算效率较低。为提升高精度SVSR的构建效率,提出一种快速搜索SVSR边界的新方法。该方法基于SVSR边界的拓扑特性,根据SVSR边界上相邻临界点之间的关联关系,构造SVSR边界快速搜索的通用数学模型。针对该模型,首先采用连续潮流确定初始SVSR边界点,然后采用预测–校正方法求解所提模型,实现SVSR边界上所有边界点的快速搜索,进而构建出SVSR边界。最后,通过WSCC 3机9节点系统和IEEE-300节点系统对所提方法的正确性和有效性进行校验,结果表明,所提方法可实现高精度SVSR边界的快速搜索。展开更多
基金Project(2016JJ2029)supported by Hunan Provincial Natural Science Foundation of ChinaProject(2016WLZC014)supported by the Open Research Fund of Hunan Provincial Key Laboratory of Network Investigational TechnologyProject(2015HNWLFZ059)supported by the Open Research Fund of Key Laboratory of Network Crime Investigation of Hunan Provincial Colleges,China
文摘Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based predictor-corrector integrators are a widely used approach for calculating the trajectories of moving atoms in direct dynamics simulations.We employ a monodromy matrix to propose a tool for evaluating the accuracy of integrators in the trajectory calculation.We choose a general velocity Verlet as a different object.We also simulate molecular with hydrogen(CO_2) and molecular with hydrogen(H_2O) motions.Comparing the eigenvalues of monodromy matrix,many simulations show that Hessian-based predictor-corrector integrators perform well for Hessian updates and non-Hessian updates.Hessian-based predictor-corrector integrator with Hessian update has a strong performance in the H_2O simulations.Hessian-based predictor-corrector integrator with Hessian update has a strong performance when the integrating step of the velocity Verlet approach is tripled for the predicting step.In the CO_2 simulations,a strong performance occurs when the integrating step is a multiple of five.
基金supported by the Natural Science Foundation of Hubei Province of China(2008CDZ047)
文摘It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_＊（κ） linear complementarity problems.This paper presents an extension of the recent variant of Mehrotra＇s second order algorithm for linear optimijation.It is shown that the iteration-complexity bound of the algorithm is O（4κ ＋ 3）√14κ ＋ 5 nlog（x0）Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization.
基金The National Natural Science Foundation of China(No.69974043)
文摘Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed.In eac h iteration,the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory.Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required.It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method.Numerical experiments on twenty-six standard test problems are made.The result s show that the proposed algorithm is stable and robust.
文摘可再生能源的波动性、随机性和需求响应的不确定性对电力系统的静态电压稳定评估带来全新挑战,静态电压稳定域（static voltage stability region,SVSR）是分析和评估含随机性和不确定性因素影响的电力系统电压稳定性的重要工具。传统基于连续潮流的SVSR构建方法虽可保证构建精度,但计算效率较低。为提升高精度SVSR的构建效率,提出一种快速搜索SVSR边界的新方法。该方法基于SVSR边界的拓扑特性,根据SVSR边界上相邻临界点之间的关联关系,构造SVSR边界快速搜索的通用数学模型。针对该模型,首先采用连续潮流确定初始SVSR边界点,然后采用预测–校正方法求解所提模型,实现SVSR边界上所有边界点的快速搜索,进而构建出SVSR边界。最后,通过WSCC 3机9节点系统和IEEE-300节点系统对所提方法的正确性和有效性进行校验,结果表明,所提方法可实现高精度SVSR边界的快速搜索。
