求解对称锥互补问题的一种非精确光滑牛顿方法

摘要

In this paper, we propose an inexact smoothing method for solving symmetric cone complementarity problem based on a one-parametric class of smoothing function which contains the FB smoothing function and the CHKS smoothing function as special cases. At each iteration, we use the GMRES iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Under suitable conditions, we obtain global convergence and local superlinear convergence of the proposed algorithm. Numerical results indicate that the proposed algorithm is effective for large-scale problem.%本文给出了一种求解对称锥互补问题的非精确光滑牛顿方法，所采用的互补函数是含一个参数且以FB和CHKS为特例的光滑函数。新方法的每步迭代中，都采用非精确牛顿方法求解由原问题产生的子问题。在一定条件下，新算法具有全局收敛和局部超线性收敛的性质。数值试验表明算法对于求解大规模对称锥互补问题是非常有效的。