Complementarity problem for η-monotone-type maps

On a homogeneous algorithm for the monotone complementarity problem

We present a generalization of a homogeneous self-dual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any \big-M" parameter or two-phase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certiicate proving infeasibility. Moreover, if the MCP is polynomiall...

A Truly Globally Convergent Newton-Type Method for the Monotone Nonlinear Complementarity Problem

Error Bounds for R0-Type and Monotone Nonlinear Complementarity Problems

The paper generalizes the Mangasarian-Ren 10] error bounds for linear complementarity problems (LCPs) to nonlinear complementarity problems (NCPs). This is done by extending the concept of R 0-matrix to several R 0-type functions, which include a subset of monotone functions as a special case. Both local and global error bounds are obtained for the R 0-type and some monotone NCPs.

Monotone Semide nite Complementarity Problems

In this paper, we study some basic properties of the monotone semide nite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive de nite matrices under certain conditions. Especially, for the monotone semide nite linear complementarity problem, the trajectory converge...

A Helly-Type Theorem for Semi-monotone Sets and Monotone Maps

We consider sets and maps defined over an o-minimal structure over the reals, such as real semi-algebraic or globally subanalytic sets. A monotone map is a multi-dimensional generalization of a usual univariate monotone continuous function on an open interval, while the closure of the graph of a monotone map is a generalization of a compact convex set. In a particular case of an identically con...