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Variational inequality formulation of the asymmetric eigenvalue complementarity problem and its solution by means of gap functions

Brás, M. ; Fukushima, M. ; Júdice, J. J. ; Rosa, S.

Pacific Journal of Optimization Vol. 8, Nº 2, pp. 197 - 215, April, 2012.

ISSN (print): 1349-8169
ISSN (online): 1348-9151

Scimago Journal Ranking: 0,47 (in 2012)

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Abstract
In this paper, the solution of the asymmetric eigenvalue complementarity problem (EiCP) is investigated by means of a variational inequality formulation. This problem is then solved by finding a stationary point of the gap function and the regularized gap function. A nonlinear programming formulation of the EiCP results from the gap function. A hybrid algorithm combining a projection technique and a modified Josephy-Newton method is proposed to solve the EiCP by finding a stationary point of the regularized gap function. Numerical results show that the proposed method can in general solve EiCPs efficiently.