On a Variable Dimension Algorithm for the Linear Complementarity Problem

In an earlier paper we presented a variable dimension algorithm for solving the linear complementarity problem (LCP). We now extend the class of LCP’s that can be solved by this algorithm to include LCP’s with copositive plus coefficient matrices. The extension, inspired by Lemke [1965], is obtained by introducing an artificial dimension and by applying the variable dimension algorithm to the enlarged LCP

An algorithm for the linear complementarity problem with upper and lower bounds

Functional Analysis

Evolution, dynamics, and fixed points

Sign-compatible dynamics describe changes in the composition of a population driven by differences in fitness. A saturated equilibrium is a fixed point for sign-compatible dynamics where each subgroup with positive population share has highest fitness. An evolutionary stable equilibrium is a saturated equilibrium attracting all trajectories nearby, such that the Euclidean distance to it decreases monotonically. We address existence, multiplicity, and dynamical stability of fixed points of sign-compatible dynamics. A saturated equilibrium may be approximated by using a variable dimension restart algorithm for solving the nonlinear complementarity problem. Journal of Economic Literature Classification Numbers: C62, C68, C72, C73. Keywords: Sign-compatible population dynamics, saturated equilibrium, evolutionary stable equilibrium, dynamic stability, nonlinear complementarity problem.mathematical economics and econometrics