On the Solution of the Extended Linear Complementarity Problem

The extended linear complementarity problem (XLCP) has been introduced in a recent paper by Mangasarian and Pang. In the present research, minimization problems with simple bounds associated to this problem are defined. When the XLCP is solvable, their solutions are global minimizers of the associated problems. Sufficient conditions that guarantee that stationary points of the associated problems are solutions of the XLCP will be proved. These theoretical results support the conjecture that local methods for box constrained optimization applied to the associated problems could be efficient tools for solving the XLCP. Keywords. Complementarity, box constrained minimization. AMS: 90C33, 90C30 Department of Computer Science and Statistics, University of the State of S. Paulo (UNESP), C.P. 136, CEP 15054-000, S~ao Jos'e do Rio Preto-SP, Brazil. This author was supported by FAPESP (Grant 96-1552-0, 96/12503-0). E-mail: andreani@nimitz.dcce.ibilce.unesp.br y Department of Mathematics, I..