An Infeasible-Interior-Point Predictor-Corrector Algorithm for the P*-Geometric LCP

摘要

A P_*-geometric linear complementarity problem (P_*GP) as a generalization of the monotone geometric linear complementarity problem is introduced. In particular, it contains the monotone standard linear complementarity problem and the horizontal linear complementarity problem. Linear and quadratic programming problems can be expressed in a ``natural'' way (i.e., without any change of variables) as P_*GP. It is shown that the algorithm of Mizuno {it et al.} [6] can be extended to solve the P_*GP. The extended algorithm is globally convergent and its computational complexity depends on the quality of the starting points. The algorithm is quadratically convergent for problems having a strictly complementary solution.