大规模绝对值等式问题的势下降内点算法

Potential Reduction Interior Point Algorithm to Large Scale Absolute Value Equations

研究了求解一类大规模绝对值等式问题的一个新算法.首先,把绝对值等式转化为单调线性互补问题,然后结合牛顿方向和中心路径方向,给出了求解线性互补问题的一种势下降内点算法,并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解.数值实验表明此方法对求解大规模绝对值等式问题是非常有效的.

A new method for solving a class of large-scale absolute value equations has been presented in this paper. Firstly, absolute value equations are transformed into monotone linear complementary prob- lem. Then we apply potential reduction interior point algorithm to solve monotone linear complementary problem which is based on the Newton direction and centering direction. We show that this algorithm has the polynomial complexity. Numerical results show that our algorithm works very well.