A nonlinear complementarity problem for monotone functions

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

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...

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.

On the Nonlinear Complementarity Problem

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

A family of NCP functions and a descent method for the nonlinear complementarity problem

In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (...