A new method for solving Second-Order Cone Eigenvalue Complementarity Problems

Samir Adly (1) , Hadia Rammal (1)

1 XLIM-DMI - DMI

In this paper, we study numerical methods for solving eigenvalue complementarity problems involving the product of second-order cones (or Lorentz cones). We reformulate such problem to find the roots of a semismooth function. An extension of the Lattice Projection Method (LPM) to solve the second-order cone eigenvalue complementarity problem is proposed. The LPM is compared to the semismooth Newton methods, associated to the Fischer–Burmeister and the natural residual functions. The performance profiles highlight the efficiency of the LPM. A globalization of these methods, based on the smoothing and regularization approaches, are discussed.

Mots clés: Lorentz cone; Second-order cone eigenvalue complementarity problem; Semismooth Newton method; Lattice Projection Method

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Hadia Rammal. A new method for solving Second-Order Cone Eigenvalue Complementarity Problems. Journal of Optimization Theory and Applications, 2015, 165 (2), pp.563-585. ⟨10.1007/s10957-014-0645-0⟩. ⟨hal-01313130⟩