Programme



Inscription Programme Venue Hébergement


N. Pustelnik : Epigraphical projection for solving l_{1,p}-norm constrained convex optimization problems


In this presentation, we focus on a family of constraints involving linear transforms of l_{1,p}-balls. The associated projection operator generally does not have a closed form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is also enforced, in order to limit the sum of the introduced epigraphical variables to the upper bound of the original lower level set. We provide closed form expressions of the epigraphical projections associated with the Euclidean norm (p = 2) and the sup norm (p = +∞). The proposed approach is validated in the context of image restoration by making use of TV-like constraints. Experiments show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems.
(joint work with G. Chierchia, J.-C. Pesquet, B. Pesquet-Popescu)