解线性互补问题的组合同伦方法

A combined homotopy method for solving linear complementarity problem

对线性互补问题LCP(M,q)给出了全局收敛的组合同伦方法,初始点的选取只要在可行域内即可。构造了线性互补问题LCP(M,q)的组合同伦方程,并证明同伦路径存在及其全局收敛性。通过数值例子对算法加以实现,表明算法是有效的。

A global convergence combined homotopy method for solving linear complementarity problem LCP（M,q） is proposed here,where the initial points are in the feasible region.We construct the combined homotopy equation to prove the existence of the smooth path and convergence.The numerical results show the method is realizable.