A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems

Tecla de Luca (1) , Francisco Facchinei (2) , Christian Kanzow (3)

1 Fondazione Ugo Bordoni
2 Department of Computer and Systems Science [Rome]
3 Institute of Applied Mathematics

In this paper we introduce a general line search scheme which easily allows us to define and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a search direction to be used in the general scheme has to enjoy in order to guarantee global convergence, local superlinear/quadratic convergence or finite convergence. We examine in detail several different semismooth algorithms and compare their theoretical features and their practical behavior on a set of large-scale problems.

Mots clés: nonlinear complementarity problem; semismoothness; Newton's method; projected gradient method; large-scale problem

Domaines: Optimisation et contrôle [math.OC]

Tecla de Luca, Francisco Facchinei, Christian Kanzow. A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems. Computational Optimization and Applications, 2000, 16, pp.173-205. ⟨10.1023/A:1008705425484⟩. ⟨hal-01351152⟩