一种求解混合约束优化问题的半可行序列线性方程组滤子算法的局部收敛性  

Local Convergence of a Semi-feasible Sequential System of Linear Equations Filter Algorithm

作　　者：薛文娟[1,2] 沈春根[3,2] 濮定国[2] 

机构地区：[1]上海电力学院数理系,上海200090 [2]同济大学数学系,上海200092 [3]上海金融学院应用数学系,上海201209

出　　处：《应用数学》2009年第1期56-64,共9页Mathematica Applicata

基　　金：国家自然基金(10571137 ,10771162)

摘　　要：作者在[10]中提出了一种半可行序列线性规划滤子方法.它将QP-free方法推广至混合约束优化问题上,并且保持对不等式约束的可行性,对等式约束部分用滤子方法处理,从而避免了罚参数的选取.该算法只需求解四个具有相同系数矩阵的线性方程组以得到搜索方向.在一定程度上克服了序列二次规划方法的缺点.[10]中仅给出了全局收敛性.本文主要给出了该算法的局部超线性收敛性证明以及数值结果.Authors in [l0] propose a new filter algorithm using the sequential systems of linear equations,which is an infeasible QP-free method. It only needs to solve four systems of linear equations having the same nonsingular coefficient matrix. Furthermore, the X active set procedure is used in order to improve the computational effect. The global convergence of our algorithm was given in [10]. However,local convergence was not shown there. In this paper, we show its locally superlinear convergence under suitable conditions and also present some numerical results.

关 键 词：滤子 序列线性规划 线搜索 超线性收敛性 

分 类 号：O221.2[理学—运筹学与控制论]