A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problem
C. Brás, A. Fischer, J. Júdice, K. Schonefeld, S. Seifert
Abstract
In
this paper, we address the solution of the symmetric eigenvalue
complementarity problem (EiCP) by treating an equivalent reformulation
of finding a stationary point of a fractional quadratic program on the
unit simplex. The spectral projected-gradient (SPG) method has been
recommended to this optimization problem when the dimension of the
symmetric EiCP is large and the accuracy of the solution is not a very
important issue. We suggest a new algorithm which combines elements
from the SPG method and the block active set method, where the latter
was originally designed for box constrained quadratic programs. In the
new algorithm the projection onto the unit simplex in the SPG method is
replaced by the much cheaper projection onto a box. This can be of
particular advantage for large and sparse symmetric EiCPs. Global
convergence to a solution of the symmetric EiCP is established.
Computational experience with medium and large symmetric EiCPs is
reported to illustrate the efficacy and efficiency of the new algorithm.