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Using exact penalties to derive a new equation reformulation of KKT systems associated to variational inequalities

Thiago A. de André (thiandre***at***gmail.com)
Paulo J. S. Silva (pjssilva***at***ime.usp.br)

Abstract: In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We also develop a semismooth Newton method for complementarity problems based on the reformulation. We close the paper showing some preliminary computational tests comparing the proposed method with classical reformulations, based on the minimum or on the Fischer-Burmeister function.

Keywords: Exact Penalties, KKT Systems, Variational Inequalities, Nonliear Complementarity

Category 1: Complementarity and Variational Inequalities

Citation: Technical Report RT-MAC 2007-01, University of Sao Paulo, Brazil

Download: [PDF]

Entry Submitted: 03/08/2007
Entry Accepted: 03/08/2007
Entry Last Modified: 03/24/2007

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