A Smoothing Method For Linear Complementarity System

The Linear complementarity system (abbreviated as LCS) is a dynamic linear complementarity problem (abbreviated as LCP). It is consisted of an ordinary differ-ential equation, a LCP constraint condition and a boundary condition. In this thesis, we mainly consider the LCS problem with two-point boundary value (abbreviated as TPTVB) condition. During our work, we will meet two difficulties:First, the solution of the LCP constraint condition in the LCS problem is implicit. Second, the initial value and the terminal value of the LCS problem with TPBVP condition are unknown. How two deal with the two difficulties are the key to solve the LCS problem with TPBVP condition. In [46], Zheng had introduced a smoothing method to solve the LCS prob-lem with TPBVP condition. The two difficulties mentioned above are handled well in Zheng's thesis. Inspired by [46], we introduce a new smoothing method to solve the LCS problem with TPBVP condition. In the last chapter, we present some numerical experiments to show that the new method is efficient and practicable.