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A Proximal Interior Point Algorithm with Applications to Image Processing

Emilie Chouzenoux(emilie.chouzenoux***at***centralesupelec.fr)
Marie-Caroline Corbineau(marie-caroline.corbineau***at***centralesupelec.fr)
Jean-Christophe Pesquet(jean-christophe.pesquet***at***centralesupelec.fr)

Abstract: In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself are analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

Keywords: Interior point methods, proximity operator, constrained optimization, forward-backward algorithm, variable metric, line search, Armijo strategy, hyperspectral unmixing, geometry-texture decomposition

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Research report, CentraleSupélec, Université Paris-Saclay, April 1st, 2019

Download: [PDF]

Entry Submitted: 05/04/2019
Entry Accepted: 05/04/2019
Entry Last Modified: 05/04/2019

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