Second-order negative-curvature methods for box-constrained and general constrained optimization

Authors:
R. Andreani;E. G. Birgin;J. M. Martínez;M. L. Schuverdt
Affiliations:
Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Computer Science, IME-USP, University of São Paulo, São Paulo, Brazil 05508-090;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970;Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, Brazil 13081-970
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.