In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent loc...

In this paper we define the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We show that the ELCP can be viewed as a kind of unifying framework for the LCP and its various generalizations. We study the general solution set of an ELCP and we develop an algorithm to find all its solutions. We also show that the general ELCP is a...

In this paper we prove a result of complementarity problem where compact condition is somewhat relaxed.

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...

We consider an extension of the horizontal linear complementarityproblem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the bilinear objective function under a monotonicity assumption, the polyhedrality of the solution set of a ...

The fixed point problem of piecewise constant mappings in Rn is investigated. This a polyhedral complementarity problem, which generalization the linear problem. Such arose author?s research on economic equilibrium exchange models, where were considered price simplex. author proposed an original approach complementarity, made it possible to obtain simple algorithms for solving present study met...

In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematica...