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)
|