Méthodes intérieures du point proximal et du gradient pour l'optimisation convexe et conique

Abstract

Gradient (subgradient) and proximal interior methods for convex minimization have already been much studied. They are based on a proximity measure associated with the Euclidian norm. \\ In this work, we consider these methods again and we introduce another proximity measure which allows us to eliminate the constraints and to present global convergence results similar to those in the unconstrained case. \\ The results are illustrated with applications and examples, including some new simple algorithms for conic optimization problems. \\ In particular, we derive a class of interior gradient algorithms which exhibits an O(k-2) global convergence rate estimate.

Date of Award	2007
Original language	French
Supervisor	Jean-Jacques STRODIOT (Supervisor), Van Hien Nguyen (Jury) & Frank CALLIER (Jury)