## An infeasible--interior--point predictor--corrector algorithm for the $P_*$-Geometric
LCP

### M. Anitescu, G. Lesaja, F. Potra

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, Jarre and Stoer 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.

Reports on computational mathematics, No. 62/1994, Department of Mathematics, The
University of Iowa