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.

Newton method, entropy function, finite termination, smoothing approximation, vertical linear complementarity problems
Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11), Transportation Systems (jel R4)
Erasmus Research Institute of Management
ERIM Report Series Research in Management
Copyright 2002, S.I. Birbil, S-C Fang, J. Han, This report in the ERIM Report Series Research in Management is intended as a means to communicate the results of recent research to academic colleagues and other interested parties. All reports are considered as preliminary and subject to possibly major revisions. This applies equally to opinions expressed, theories developed, and data used. Therefore, comments and suggestions are welcome and should be directed to the authors.
Erasmus Research Institute of Management

Birbil, S.I, Fang, S-C, & Han, J. (2002). On the Finite Termination of An Entropy Function Based Smoothing Newton Method for Vertical Linear Complementarity Problems (No. ERS-2002-72-LIS). ERIM Report Series Research in Management. Erasmus Research Institute of Management. Retrieved from