对称锥权互补问题的正则化非单调非精确光滑牛顿法

A Regularized Nonmonotone Inexact Smoothing Newton Algorithm for Weighted Symmetric Cone Complementarity Problems

该文提出正则化非单调非精确光滑牛顿法求解对称锥权互补问题(wSCCP).算法将正则化参数视为一个独立变量,因此它与许多现有的算法相比,更简单易实现.在每次迭代中,算法只需求得方程组的近似解.另外,算法中的非单调线搜索包含了两种常用的非单调形式.在单调假设下,证明算法全局收敛且局部二阶收敛.最后,一些数值结果表明了算法的有效性.

In this paper,we propose a regularized nonmonotone inexact smoothing Newton algorithm for solving the weighted symmetric cone complementarity problem(wSCCP).In the algorithm,we consider the regularized parameter as an independent variable.Therefore,it is simpler and easier to implement than many available algorithms.At each iteration,we only need to obtain an inexact solution of a system of equations.Moreover,the nonmonotone line search technique adopted in our algorithm includes two popular nonmonotone search schemes.We prove that the algorithm is globally and locally quadratically convergent under suitable assumptions.Finally,some preliminary numerical results indicate the effectiveness of our algorithm.