A new method for solving second-order cone eigenvalue complementary problem

par Hadia Rammal (XLIM-DMI, Université de Limoges)

jeudi 16 mai 2013, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

Eigenvalue complementarity problem EiCP with nonnegativity constraints has become a fruitful discipline within mathematical programming. In this paper, we extend EiCP to problem where the nonnegative orthant, i.e., the Pareto cone is replaced by the product of second order cones SOC. We reformulate such problem to find the roots of a semismooth function. Furthermore, we generalize the Lattice Projection Method LPM proposed first in [1] to solve the second order cone eigenvalue complementarity problem SOCEiCP. The originality of this work, in comparison with [1], is that we use a globalization of the semismooth Newton method SNM to approximate the Lorentz eigenvalues. Surprisngly, this kind of subject has never been studied before due to the difficulty of this problem in the sense that the Lorentz spectrum is not always finite. Finally, LPM is then compared to the semismooth Newton methods with line search: SNM$_{\min}$ and SNM$_{\rm FB}$, by using the performance profiles as a comparison tool. The numerical experiments highlight that the LPM solver is efficient and robust for solving SOCEiCP. [1]- A New Method for Solving Pareto Eigenvalue Complementarity Problems, to appear in Computational Optimization and Applications.