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An L1 Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints

Zoumana Coulibaly (zoumana.coulibaly***at***gerad.ca)
Dominique Orban (dominique.orban***at***gerad.ca)

Abstract: We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the method allows for a unified treatment of both general, unstructured, and structured degenerate problems, such as problems with complementarity constraints, with no changes to accommodate one class or the other. Numerical results on a standard test set illustrate the efficiency and robustness of the approach.

Keywords: mpcc, complementarity constraints, L1-penalty function, Interior-Point Method, Elastic variables, Degeneracy, strong stationarity, symmetric indefinite factorization

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Cahier du Gerad G-2009-74, GERAD, HEC Montréal 3000, chemin de la Côte-Sainte-Catherine Montréal (Québec) Canada H3T 2A7, 11/2009

Download: [PDF]

Entry Submitted: 11/13/2009
Entry Accepted: 11/13/2009
Entry Last Modified: 11/13/2009

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