A method for the solution of minimization problems with simple bounds is presented. Global convergence of a general scheme requiring the approximate solution of a single linear system at each iteration is proved and a superlinear convergence rate is established without requiring the strict complementarity assumption. The algorithm proposed is based on a simple, smooth unconstrained reformulation of the bound constrained problem and may produce a sequence of points that are not feasible. Numerical results and comparison with existing codes are reported.

A truncated Newton algorithm for large scale box constrained optimization / Facchinei, Francisco; Lucidi, Stefano; Palagi, Laura. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 12:4(2002), pp. 1100-1125. [10.1137/s1052623499359890]

A truncated Newton algorithm for large scale box constrained optimization

FACCHINEI, Francisco;LUCIDI, Stefano;PALAGI, Laura
2002

Abstract

A method for the solution of minimization problems with simple bounds is presented. Global convergence of a general scheme requiring the approximate solution of a single linear system at each iteration is proved and a superlinear convergence rate is established without requiring the strict complementarity assumption. The algorithm proposed is based on a simple, smooth unconstrained reformulation of the bound constrained problem and may produce a sequence of points that are not feasible. Numerical results and comparison with existing codes are reported.
bound constrained problem; conjugate gradient; newton method; nonmonotone line search; penalty function
01 Pubblicazione su rivista::01a Articolo in rivista
A truncated Newton algorithm for large scale box constrained optimization / Facchinei, Francisco; Lucidi, Stefano; Palagi, Laura. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - 12:4(2002), pp. 1100-1125. [10.1137/s1052623499359890]
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