A non-interior continuation method for generalized linear complementarity problems

In this paper, we propose a non-interior continuation method for solving generalized linear complementarity problems (GLCP) introduced by Cottle and Dantzig. The method is based on a smoothing function derived from the exponential penalty function first introduced by Kort and Bertsekas for constrained minimization. This smoothing function can also be viewed as a natural extension of Chen-Mangasarian's neural network smooth function. By using the smoothing function, we approximate GLCP as a family of parameterized smooth equations. An algorithm is presented to follow the smoothing path. Under suitable assumptions, it is shown that the algorithm is globally convergent and local Q-quadratically convergent. Few preliminary numerical results are also reported.