解非线性互补问题的光滑牛顿方法  

Smooth Newton Method for Nonlinear Complementarity Problems

作　　者：俞昊东 

机构地区：[1]上海立信会计金融学院统计与数学学院,上海201620

出　　处：《数学的实践与认识》2016年第23期216-224,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11401384)

摘　　要：由于退化解会导致再生方程的奇异性,非线性互补问题的求解通常采用基于半光滑技术的广义牛顿法.基于2-正则性的概念,提出了一类利用光滑互补函数求解互补问题的光滑牛顿算法.算法采用积极集技术,能在解的附近估计出退化指标,并把原问题降阶为一个非奇异方程组,从而保证了迭代效率.算法具有整体收敛性和局部超线性收敛性,数值实验显示算法是有效的.Nonlinear complementarity problems are usually solved by generalized Newton methods to avoid the singularity of the reformulation equations caused by the degenerate solutions. In this paper, based on the concept of 2-regularity, a smooth Newton method, which uses smooth complementarity functions, is proposed to solve complementarity problems. The algorithm introduces the active-set technique, and can estimate the degenerate indices correctly when near the solution. By reducing the original problem to a non-singular reduced equation, the computation efficiency of the Newton method is guaranteed. This method has global convergence and local superlinear convergence. Finally, some numerical results are listed to show the efficiency of the algorithm.

关 键 词：非线性互补问题 退化解 2-正则性 光滑互补函数 

分 类 号：O242.23[理学—计算数学]