Seminar Details
2016-11-22 (16:30) : A line-search based proximal algorithm for convex and non-convex optimization, with applications to image processing
At CORE (room C.035)
Organized by Mathematical Engineering
Speaker :
Ignace Loris (ULB)
Abstract :
A novel iterative algorithm for the solution of convex or non-convex
optimization problems is presented. In particular, the objective
function is assumed to be the sum of a differentiable (possibly
non-convex) part and a convex (possibly non-differentiable) part. The
proposed algorithm is based on an Armijo line-search rule and uses the
gradient of the smooth part and the proximal operator of the non-smooth
part. However, the proximal operator does not have to be computed
exactly and verifiable criteria for its inexact computation are given in
some cases of practical interest.
In general we prove that all limit points of the iterates are
stationary, while in the special case of a convex objective function we
prove the convergence of the whole sequence to a minimizer. In the
non-convex case, we also show convergence if the objective function
satisfies the Kurdyka- Lojasiewicz property at each point of its domain.
Finally, the algorithm is applied to a wide range of image
reconstruction problems.