一种求解非线性互补问题的filter内点算法

摘要

利用 Armijio 条件和信赖域方法，构造新的价值函数。首次将内点算法与 filter技术结合起来，提出一种求解非线性互补问题的新算法，即 filter 内点算法。在主算法中使用Armijio 型线搜索求取步长，在修复算法中使用信赖域方法进行适当控制以保证算法的收敛性。文章还讨论了算法的全局收敛性。最后用数值实验表明了该方法是有效的。%A new merit function is constructed by using Armijio conditions and the trust region method. Then firstly combining the interior-point method with filter technique, we propose a new algorithm to solve nonlinear complementarity problem. In the main arithmetic, step length is produced by Armijio type line search, and in the repair algorithm, trust region method is used to properly control so as to ensure the convergence of the algorithm. We also discuss the global convergence of the algorithm. Finally, the numerical experiments show that the method is effective.