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PIPA: A Proximal Interior Point Algorithm for Large-Scale Convex Optimization

Giovedì 11 ottobre 2018, ore 14:00, laboratorio Zironi, primo piano, edificio Matematica, Dipartimento FIM, Modena

Relatore: Marie-Caroline Corbineau (Centre pour la Vision Numérique, CentraleSupélec - Paris)

Abstract: Interior point methods have been known for decades to be useful for the resolution of small to medium size constrained optimization problems. These approaches have the benefit of ensuring feasibility of the iterates through a logarithmic barrier. We propose to incorporate a proximal forward-backward step in the resolution of the barrier subproblem to account for non-necessarily differentiable terms arising in the objective function. The combination of this scheme with a recently introduced linesearch strategy gives rise to the so-called Proximal Interior-Point Algorithm (PIPA) suitable for the minimization of the sum of a smooth convex function and a non-smooth convex one under general convex constraints. The convergence of PIPA iterates is secured under mild assumptions.
As demonstrated by numerical experiments carried out on two image processing applications, the proposed method is efficient in solving large-scale convex optimization problems. In particular, PIPA compares favorably with the ADMM algorithm on both examples.

Ospiti: Marco Prato

[Ultimo aggiornamento: 04/10/2018 13:36:37]