On the asymmetric eigenvalue complementarity problem

J. Júdice, H. Sherali, I. Ribeiro and S. Rosa

Abstract

In this paper, we discuss the Eigenvalue Complementarity Problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution for the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate merit function on a convex set \Omega defined by linear constraints. A sufficient condition for a stationary point of this function on \Omega to be a solution of the EiCP is presented. A branch-and-bound procedure is developed for finding a global minimum of this merit function on \Omega. In addition, a sequential enumerative algorithm for the computation of the minimum and maximum eigenvalues is also discussed. Computational experience is included to highlight the efficacy and efficiency of the proposed methodologies to solve the asymmetric EiCP.