线性互补问题的序列凸近似方法

Sequential Convex Approximation Approach to Linear Complementarity Problems

线性互补问题是一类有着广泛应用背景的重要数学问题,本文主要讨论其求解方法.本文首先将线性互补问题等价转化为目标函数含有DC函数(两个凸函数的差函数)的优化问题,然后对该DC问题目标函数的第二部分凸函数进行线性化,得到一列凸近似子问题.本文证明该列子问题的解的聚点是线性互补问题的稳定点.

The main purpose of this work is to solve the linear complementarity problem, which is an important mathematical problem with wide applications. The linear complementarity problem is firstly reformulated into an optimization problem with a DC （difference of convex） objective function, then the second term in the DC objective function is linearized in order to produce a sequence of convex sub - problems. It is demonstrated later that all the cluster points of optimal solutions of these convex sub - problems are stationary points of the original linear complementarity problem.