Summary: 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 S. Mizuno, F. Jarre and J. Stoer [Appl. Math. Optimization 33, No. 3, 315-341 (1996; Zbl 0846.90112)] 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.