A new algorithm is presented for solving a system of linear inequalities. Starting at any point by solving a least squares problem we can either obtain a feasible point or determine that no solution exists.
An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace def...An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.展开更多
For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is ded...For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.展开更多
针对锁相环同步的弱连接电压源变流器(weakgrid connected voltage source converter,WG-VSC)系统的暂态稳定问题,该文首先应用线性矩阵不等式优化法构建WG-VSC系统的最大估计吸引域(largest estimated domain of attraction,LEDA),并将...针对锁相环同步的弱连接电压源变流器(weakgrid connected voltage source converter,WG-VSC)系统的暂态稳定问题,该文首先应用线性矩阵不等式优化法构建WG-VSC系统的最大估计吸引域(largest estimated domain of attraction,LEDA),并将LEDA与基于LaSalle不变集定理的能量函数法和平方和规划法构建的LEDA进行详细对比,验证了所提方法在刻画LEDA方面具有更低的保守性。然后从保证故障穿越控制过程中的锁相环暂态同步稳定作为切入点,首次提出WG-VSC系统在电网对称故障大扰动下的有功/无功电流设定值可行域概念,并基于线性矩阵不等式方法刻画的LEDA,提出该可行域的求解算法,分析了典型参数对该电流设定值可行域的影响。该可行域为故障过程中的有功和无功电流设定值提供了切实可行的指导依据。最后在PSCAD/EMTDC中搭建了基于详细开关模型的WG-VSC系统仿真算例,通过多种暂态仿真工况验证了该文所构建的LEDA和电流设定值可行域的有效性和可行性。展开更多
基金The project supported by National Natural Science Foundation of China.
文摘A new algorithm is presented for solving a system of linear inequalities. Starting at any point by solving a least squares problem we can either obtain a feasible point or determine that no solution exists.
基金Supported by The Natural Science Fundations of China and Jiangsu
文摘An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.
文摘For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.
文摘针对锁相环同步的弱连接电压源变流器(weakgrid connected voltage source converter,WG-VSC)系统的暂态稳定问题,该文首先应用线性矩阵不等式优化法构建WG-VSC系统的最大估计吸引域(largest estimated domain of attraction,LEDA),并将LEDA与基于LaSalle不变集定理的能量函数法和平方和规划法构建的LEDA进行详细对比,验证了所提方法在刻画LEDA方面具有更低的保守性。然后从保证故障穿越控制过程中的锁相环暂态同步稳定作为切入点,首次提出WG-VSC系统在电网对称故障大扰动下的有功/无功电流设定值可行域概念,并基于线性矩阵不等式方法刻画的LEDA,提出该可行域的求解算法,分析了典型参数对该电流设定值可行域的影响。该可行域为故障过程中的有功和无功电流设定值提供了切实可行的指导依据。最后在PSCAD/EMTDC中搭建了基于详细开关模型的WG-VSC系统仿真算例,通过多种暂态仿真工况验证了该文所构建的LEDA和电流设定值可行域的有效性和可行性。
