Artículos de revistas
NEW ALGORITHMS FOR MAXIMIZATION OF CONCAVE FUNCTIONS WITH BOX CONSTRAINTS
Registro en:
Rairo-recherche Operationnelle-operations Research. Dunod, v. 26, n. 3, n. 209, n. 236, 1992.
0399-0559
WOS:A1992JL81700001
Autor
FRIEDLANDER, A
MARTINEZ, JM
Institución
Resumen
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. 26 3 209 236