一种求解P_*(κ)阵线性互补问题的宽邻域内点算法

A Wide-Neighborhood Interior-Point Algorithm for the P_*(κ)-Matrix Linear Complementarity Problem

基于线性规划宽邻域内点算法的基本思想,对P*(κ)阵线性互补问题提出了一种基于宽邻域N∞-(β)的势函数约减算法.该算法的每一次迭代都通过求解一个线性方程组得到迭代方向,并利用势函数来选取步长,使得迭代前后势函数按一固定量减少,从而使对偶间隙有固定的减少.证明了算法的迭代复杂性为O((κ+1)nt).

This paper describes a new wide-neighborhood potential reduction interior-point algorithm for P＊ （κ）-matrix linear complementarity problem, using the neighborhood N∞^-（β） which is much wider. The algorithm is based on the idea of wide-neighborhood algorithm for linear programming. At each iteration, search direction can be computed as a solution of a linear system, and uses a potential function to choose a step size, so this algorithm decreases the potential function by a fixed amount, under the condition that the duality gap decreases at the same. Finally, we prove that its iteration complexity is O（ （κ＋ 1） nt） under general conditions.