The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a path-generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length acceptance criterion and a non-monotone pathsearch are then used to choose the next iterate. The algorith...

We propose a family of directions that generalizes many directions proposed so far in interiorpoint methods for the SDP (semide nite programming) and for the monotone SDLCP (semide nite linear complementarity problem). We derive the family from the Helmberg-Rendl-Vanderbei-Wolkowicz/KojimaShindoh-Hara/Monteiro direction by relaxing its \centrality equation" into a \centrality inequality." Using...

A new necessary and sufficient condition for the row W-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row W-property, which extend the error bounds given in [2, 10] for the P-matrix linear complementarity problem, respectively. We show that one of the new error ...

For the extended linear complementarity problem 11], we introduce and characterize column-suuciency, row-suuciency, and P-properties. These properties are then specialized to the vertical , horizontal, and mixed linear complementarity problems.

Regularization methods for the solution of nonlinear complementarity problems are standard methods for the solution of monotone complementarity problems and possess strong convergence properties. In this paper, we replace the monotonicity assumption by a P0-function condition. We show that many properties of regularization methods still hold for this larger class of problems. However, we also p...

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation|one that has fewer constraints than the \stan-dard" QP formulation|is available. We mention several instances of this class, including the known case in which the coeecient matrix in the LCP...