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

Authors
  • ANDREANI, R.
  • BIRGIN, E. G.
  • MARTINEZ, J. M.
  • SCHUVERDT, M. L.
Publication Date
Jan 01, 2010
Source
Biblioteca Digital da Produção Intelectual da Universidade de São Paulo (BDPI/USP)
Keywords
Language
English
License
Unknown
External links

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.

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