Solving Eigenvalue Complementarity Problems by the Globalized BFGS Method Based on the Hyperplane Projection Method

The first idea for solving the Eigenvalue Complementarity Problem (EiCP) is to transform it into a Nonlinear Complementarity Problem (NCP) or a Variational Inequality (VI) over a sim- plex. Since the resulting problems are non-monotone, most of the robust solvers are unsuitable for solving them. In this paper, we use the globally convergent BFGS method proposed in [1] to solve the EiCP. In fact, the globalization technique applied to the BFGS method is on the basis of the hyperplane projection method.