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|Title:||New algorithms for maximization of concave functions with box constraints|
Martínez, J. M.
|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 , 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.|
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 inc
|metadata.dc.description.abstractalternative:||Nouveaux algorithmes pour la maximisation de fonctions concaves à variables bornées. Ce travail considère le problème de maximiser une fonction concave differentiable soumise à des restrictions de bornes sur les variables et dont le gradient satisfait aux|
|Citation:||Rairo-recherche Operationnelle-operations Research. Dunod, v. 26, n. 3, n. 209, n. 236, 1992.|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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