Variational Inequality Formulation of the Asymmetric Eigenvalue Complementarity Problem and Its Solution by Means of Gap Functions

Citation:
Brás, C. P., M. Fukushima, J. J. Júdice, and S. S. Rosa. "Variational Inequality Formulation of the Asymmetric Eigenvalue Complementarity Problem and Its Solution by Means of Gap Functions." Pacific Journal of Optimization. 8.(2) (2012): 197-215.

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.

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