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.