A new method for solving Pareto eigenvalue complementarity problems

Samir Adly (1) , Hadia Rammal (1)

1 XLIM-DMI - DMI

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNMmin and SNMFB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201-213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125-137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.

Mots clés: Bi-eigenvalue complementarity problems; Lattice Projection Method; Semismooth Newton Method; Complementarity problems; One-constrained eigenvalue problems; Complementarity functions

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Hadia Rammal. A new method for solving Pareto eigenvalue complementarity problems. Computational Optimization and Applications, 2013, 55 (3), pp.703-731. ⟨10.1007/s10589-013-9534-y⟩. ⟨hal-00908170⟩