Global Convergence Properties of Some Iterative Methods for Linear Complementarity Problems

The subject of this work is a class of iterative methods for solving the linear complementarily problem (LCP). These methods are based on a reformulation of the LCP consisting of a (usually) differentiable system of nonlinear equations, to which Newton’s method is applied. Thus, the algorithms are locally Q-quadratically convergent. Furthermore, global convergence results for these methods are proved for LCPs associated with R₀-, nondegenerate, and P-matrices. Finally, some promising numerical results are reported for both constructed and randomly generated problems.