求解非线性互补问题的非单调共轭梯度法

AN ON-MONOTONE-STEP CONJUGATE GRADIENT ALGORITHM FOR SOLVING NCP

利用非线性互补问题（NCP）的F-B价值函数，基于PRP＋型共轭梯度算法，结合Gu N．Z．的新的非单调搜索技术提出新的利用F-B价值函数求解非线性互补问题（NCP）的非单调共轭梯度算法，该算法保持了共轭梯度算法和非单调数据的优良性质．在适当的条件下，证明了算法的全局收敛性，数值实验证明是有效的，适合解决大规模非线性互补问题．

Nonlinear complementarity problem can be reformulated as an unconstrained optimization problem by using F-B merit function.Based on PRP＋type conjugate gradient method,by combining with Gu N.Z.non-monotone-step line search technique,we propose a new non-monotone-step conjugate gradient algorithm for solving nonlinear complementarity problem via F -B merit function.The new algorithm has excellent？quality of keeping？conjugate gradient method and non -monotone -step line search technique.Under some reasonable conditions,it is proved that the algorithm is globally convergent.Numerical experiments show that the new algorithm is effective,suitable to solve large scale nonlinear complementarity problems.