Using vector divisions in solving the linear complementarity problem. (English) Zbl 1238.65053
Summary: The linear complementarity problem is to find a vector in satisfying , , , where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems.
|65K05||Mathematical programming (numerical methods)|
|90C33||Complementarity and equilibrium problems; variational inequalities (finite dimensions)|
|65H10||Systems of nonlinear equations (numerical methods)|