求解非线性P_0互补问题的非单调磨光算法  

NON-MONOTONE SMOOTHING ALGORITHM FOR SOLVING NONLINEAR P_0 COMPLEMENTARITY PROBLEMS

作　　者：袁敏[1] 万中[1] 

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《计算数学》2014年第1期35-50,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助(基金号:71221061;71071162)项目;湖南省自然科学基金(基金号:13JJ3002)项目

摘　　要：提出了一种新的磨光函数,在分析它与已有磨光函数不同特性的基础上,研究了将它用于求解非线性P_0互补问题时,其磨光路径的存在性和连续性,进而设计了求解一类非线性P_0互补问题的非单调磨光算法.在适当的假设条件下,证明了该算法的全局收敛性和局部超线性收敛性.数值算例验证了算法的有效性.In this paper, a new smoothing function is constructed, and on the basis of its prop- erties, the existence and the continuity of smoothing path are investigated when this s- moothing function is employed to solve a nonlinear P0 complementarity problem. Then, a non-monotone smoothing algorithm is developed to solve the nonlinear P0 complementarity problems. Under suitable assumptions, both global convergence and super-linear conver- gence are established for the developed algorithm. Numerical experiments show that the algorithm is efficient.

关 键 词：互补问题 磨光算法 全局收敛性 超线性收敛性 

分 类 号：O224[理学—运筹学与控制论]