On Convex optimization without convex representation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Optimization Letters Année : 2011

On Convex optimization without convex representation

Résumé

We consider the convex optimization problem P: min { f(x): x in K} where "f" is convex continuously differentiable, and K is a compact convex set in Rn with representation {x: g_j(x) >=0, j=1,;;,m} for some continuously differentiable functions (g_j). We discuss the case where the g_j's are not all concave (in contrast with convex programming where they all are). In particular, even if the g_j's are not concave, we consider the log-barrier function phi_\mu with parameter \mu, associated with P, usually defined for concave functions (g_j). We then show that any limit point of any sequence (x_\mu) of stationary points of phi_\mu, \mu ->0, is a Karush-Kuhn-Tucker point of problem P and a global minimizer of f on K.
Fichier principal
Vignette du fichier
log-corrige.pdf (140.97 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00495396 , version 1 (25-06-2010)
hal-00495396 , version 2 (28-03-2011)
hal-00495396 , version 3 (28-01-2014)

Identifiants

Citer

Jean-Bernard Lasserre. On Convex optimization without convex representation. Optimization Letters, 2011, 5 (4), p. 549-556. ⟨hal-00495396v3⟩
299 Consultations
227 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More