Bot, Radu Ioan ; Grad, Sorin-Mihai ; Wanka, Gert : Generalized Moreau-Rockafellar results for composed convex functions

Author(s):

Bot, Radu Ioan
Grad, Sorin-Mihai
Wanka, Gert

Title:

Generalized Moreau-Rockafellar results for composed convex functions

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 16, 2007

Mathematics Subject Classification:

90C25			[ Convex programming ]
49N15			[ Duality theory ]
65K10			[ Optimization and variational techniques ]

Abstract:

We give two generalized Moreau-Rockafellar-type results for the sum of a convex function with the composition of convex functions in separated locally convex spaces. Then we equivalently characterize the stable strong duality for composed convex optimization problems through two new regularity conditions, which also guarantee two formulae of the subdifferential of the mentioned sum of functions. We also treat some special cases, rediscovering older results in the literature. A discussion on the topological assumptions for the vector function used in the composition closes the paper.

Keywords:

conjugate functions, Moreau-Rockafellar results, regularity conditions, stable strong duality, composed convex functions

Language:

English

Publication time:

9 / 2007