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

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...

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Bibliographic Details
Published in:Computational optimization and applications 2010-03, Vol.45 (2), p.209-236
Main Authors: Andreani, R., Birgin, E. G., Martínez, J. M., Schuverdt, M. L.
Format: Article
Language:English
Subjects:
Algorithms
Convex and Discrete Geometry
Lagrange multiplier
Management Science
Mathematics
Mathematics and Statistics
Methods
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Studies
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Summary: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.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-009-9240-y