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.

It is well known that variational inequalities are systematically used in the theory of many practical problems related to ”equilibrium”. The equilibrium is an important state considered in Physics, Engineering, Sciences and Economics and even in Biology, [5], [37], [38], [24], [56]. When a variational inequality is defined on a closed convex set, which is in particular a closed convex cone, in...

In this paper, we extended the result about the error estimation for linear complementarity problem to the extended linear complementarity problem (ELCP) in management equilibrium modeling. More precisely, we first present that the level set of a computable residual function is bounded, and give error estimation in level set. Based on this, we use this residual function to establish a global er...

We introduce the new concept of d-orientation sequence for continuous functions. It is shown that if there does not exist a d-orientation sequence for a continuous function, then the corresponding complementarity problem (CP) has a solution. We believe that such a result characterizes an intrinsic property of CPs. As the concept of ``exceptional family of elements'', the notion of ``d-orientati...

In this paper, we propose a Big-? smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory deened by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has a solution. The method has been tested on the P 0 matrix linear complementarity problem with unbou...

This report gives an overview of the linear complementarity problem, as a special case of mathematical programming with equilibrium constraints. The interior point method and two versions of Lemke’s method are reviewed, as methods for solving the linear complementarity problem. The report concludes with a description of the Stackelberg game and the bimatrix game as possible applications of math...

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natura...