Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/65341
Type: Artigo de periódico
Title: NEW ALGORITHMS FOR MAXIMIZATION OF CONCAVE FUNCTIONS WITH BOX CONSTRAINTS
Author: FRIEDLANDER, A
MARTINEZ, JM
Abstract: This paper considers the problem of maximizing a differentiable concave function subject to bound constraints and a Lipschitz condition on the gradient, using active set strategies. A general model algorithm for this problem is proposed. The algorithm includes a procedure for deciding when to leave a face of the polytope without having reached a stationary point relative to that face, guaranteing that return to that face excludes a neighborhood of fixed size of the current point. Mild conditions are required to abandon a face, which may possibly never be visited again, and we show that any face may be revisited al most a finite number of times. We show a bound for this quantity. We prove global convergence for this algorithm and we also show that it identifies the correct optimal face in a finite number of iterations, even without any nondegeneracy condition, when we use the "chopped gradient" introduced in [10], as the direction on which we leave any face. We combine the active set strategy proposed with a gradient projection method following the approach of More-Toraldo ([23,24]), in order to accelerate the identification of the correct optimal face.
Subject: OPTIMIZATION
BOX CONSTRAINTS
Country: França
Editor: Dunod
Rights: aberto
Date Issue: 1992
Appears in Collections:Unicamp - Artigos e Outros Documentos

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