On the Computation of All Eigenvalues for the Eigenvalue Complementarity Problem
Luís M. Fernandes, Joaquim J. Júdice, Hanif D. Sherali, Masao Fukushima
Abstract
In
this paper, a parametric algorithm is introduced for computing all
eigenvalues for two Eigenvalue Complementarity Problems discussed in
the literature. The algorithm searches a finite number of nested
intervals [l, u] in such a way that, in each iteration, either an eigenvalue is computed in [l, u] or a certificate of nonexistence of an eigenvalue in [l, u] is
provided. A hybrid method that combines an enumerative method [5] and a
semi-smooth algorithm [1] is discussed for dealing with the Eigenvalue
Complementarity Problem over an interval [ l, u]. Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.
Keywords: Eigenvalue Problems, Complementarity Problems, Nonlinear Programming, Global Optimization.