A penalty method for solving the MPCC problem

The main goal of this work is to solve Mathematical Program with Complementarity Constraints (MPCC) using the penalty technique from the nonlinear optimization. The hyperbolic penalty method is used to solve the nonlinear reformulation of the MPCC in which the complementarity constraints are gathered into a single constraint and included in the penalty function. Three algorithms were implemented in MATLAB language using the penalty technique, two of them use the hyperbolic penalty method in two different approaches and the other implements the l(1) penalty. Numerical experiments are performed using a set of AMPL test problems from the MacMPEC database. A performance comparative analysis with respect to some metrics is carried out.- The third author was supported by ALGORITMI R&D Center under the project PEst-UID/CEC/00319/2013 financed by Fundacao para a Ciencia e Tecnologia (FCT-Portugal).The work is also supported by PEst-OE/MAT/UI4080/2014. The authors are very grateful to all the financial support. The authors are very grateful to two referees for many constructive comments and remarks.