Subdifferential Test for Optimality

Florence Jules (1) , Marc Lassonde (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the function is convex.

Domaines: Optimisation et contrôle [math.OC]; Analyse fonctionnelle [math.FA]

Florence Jules, Marc Lassonde. Subdifferential Test for Optimality. Journal of Global Optimization, 2013, pp.1-6. ⟨10.1007/s10898-013-0078-6⟩. ⟨hal-00761658⟩