By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite number of iterations, under some conditions milder than those assumed in literature. Some computational results are included to illustrate the potential of this approach.

Entropy function, Finite termination, Newton method, Smoothing approximation, Vertical linear complementarity problems
Econometric Institute Research Papers
Erasmus School of Economics

Fang, S-C, Han, J, Huang, Z, & Birbil, S.I. (2002). On the finite termination of an entropy function based smoothing Newton method for vertical linear complementarity problems (No. EI 2002-50). Econometric Institute Research Papers. Retrieved from