非线形互补问题的障碍函数法

Barrier Function for the Nonlinear Complementarity Problem

将非线形互补问题转化为约束的优化问题,在已经的利用内点障碍函数方法求解约束优化问题的基础上,提出了利用障碍函数方法求解非线形互补问题的采用序列无约束最小化方法(SUMT)的算法,并利用障碍函数的单调性证明了算法的全局收敛性.最后得出的数值试验表明了算法具有良好的适宜性和强收敛性.

This paper converts the nonlinear complementarity problems into the question of constrained optimization, and then puts forward we introduce Sequential Unconstrained Minimization Technique （SUMT） algorithm to solve the nonlinear complementarity problems using barrier functions on the basis of the existing solutions to constrained optimization with existing barrier function. Furthermore, with the monotonicity of barrier functions, this paper proves the convergence of the algorithm. Finally, a numerical example is given to illustrate the good regularity and strong convergence of this algorithm.