大规模非负线性最小二乘问题的一个新算法  

A new method for large-scale nonnegative linear least squares problems

作　　者：雍龙泉[1,2] 刘三阳[1] 张建科[3] 周涛[4] 

机构地区：[1]西安电子科技大学应用数学系,西安710071 [2]陕西理工学院数学与计算机科学学院,陕西汉中723001 [3]西安邮电学院理学院,西安710121 [4]宁夏医科大学理学院,银川750004

出　　处：《兰州大学学报（自然科学版）》2012年第5期114-117,123,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(60974082;81160183);陕西省教育厅科研计划项目(12JK0863;11JK1051)

摘　　要：研究了求解非负线性最小二乘问题的一个新算法.首先把非负线性最小二乘转化为单调线性互补问题,然后基于牛顿方向和中心路径方向,给出了求解单调线性互补问题的一种势下降内点算法,并证明该算法经过有限次迭代之后收敛到原问题的一个最优解.数值实验表明此方法对求解大规模非负线性最小二乘问题是非常有效的.A new method for solving large-scale nonnegative linear least square problems was presented. First, a nonnegative linear least squares problem was transformed into a monotone linear complementarity problem. Then the potential-reduction interior point algorithm was applied to the monotone linear complementarity problem based on the Newton direction and centering direction. We showed that this algorithm stopped at an optimal solution after a finite number of iterations. The numerical results reported here demonstrated a very good computational performance on nonnegative linear least squares problems.

关 键 词：大规模非负线性最小二乘问题 单调线性互补问题 势下降内点算法 

分 类 号：O221[理学—运筹学与控制论]