Numerical validation of solutions of linear complementarity problems (Q1805871)

The authors propose a validation method for solutions of linear complementary problems of the form \[ Mx+ q\geq 0,\quad x\geq 0,\quad (Mx+ q)^Tx= 0. \] The study of the authors is based on the mean value theorem for absolutely continuous functions and the reformulation of linear complementarity problems as systems of nonsmooth nonlinear equations. The given validation procedure consists of two sufficient conditions that can be tested on a digital computer. Numerical tests are presented.