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A quasi-Newton strategy for the sSQP method for variational inequality and optimization problems

Damián Fernández (dfernandez***at***famaf.unc.edu.ar)

Abstract: The quasi-Newton strategy presented in this paper preserves one of the most important features of the stabilized Sequential Quadratic Programming method, the local convergence without constraint qualifications assumptions. It is known that the primal-dual sequence converges quadratically assuming only the second-order sufficient condition. In this work, we show that if the matrices are updated by performing a minimization of a Bregman distance (which includes the classic updates), the quasi-Newton version of the method converges superlinearly without introducing further assumptions. Also, we show that even for an unbounded Lagrange multiplier set, the generated matrices satisfies a bounded deterioration property and the Dennis-Mor\'e condition.

Keywords: Stabilized sequential quadratic programming, quasi-Newton methods, Karush-Kuhn-Tucker system, Variational inequality

Category 1: Nonlinear Optimization (Quadratic Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 10/13/2010
Entry Accepted: 10/13/2010
Entry Last Modified: 09/12/2011

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