线性互补问题在宽邻域下的局部二次收敛算法  

A Quadratically Convergent Algorithm in a Wide Neighborhood for Linear Complementarity Problems

作　　者：马晓珏[1,2] 刘红卫[1] 

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071 [2]西安邮电大学理学院,陕西西安710121

出　　处：《应用数学》2017年第2期337-343,共7页Mathematica Applicata

基　　金：国家自然科学基金(11301415;61303030);陕西省教育厅专项科研基金资助项目(15JK1651)

摘　　要：艾文宝(2004)的宽邻域算法弥补了内点法在理论和实践表现之间的差异.基于这个算法的优越性,将其推广到线性互补问题中.新算法在一次迭代中,采用两个方向的线性组合作为新方向,并以满步长到达下一个点.可以证明,该算法具有O(n^(1/2)L)的理论复杂度,这是迄今为止最好的复杂度结果.同时,在假设线性互补问题存在严格互补解的前提下,证明算法具有局部二次收敛性.最后,数值实验说明算法是有效的.The algorithm, proposed by AI（2004） in his new wide neighborhood, can fill the gap between in theory and in practice for primal-dual interior-point methods. Based on the point, it is generalized to solve linear complementarity problems. In each iteration of the algorithm of AI, a linear combined direction is used, and a full step size along the direction is adequate for the next iterate point. It can be proved that the algorithm has an O（n（1/2） L） complexity bound, which is the best result so far. Furthermore,its quadratic convergence can be shown under the assumptation that a strictly complementary solution exists. Numerical tests show that it is effective.

关 键 词：原-对偶内点法 宽邻域 线性互补问题 二次收敛 

分 类 号：O221.1[理学—运筹学与控制论]