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Reinterpreting EMML as Mirror Descent for Constrained Maximum Likelihood Estimation
Antonin Clerc, Ségolène Martin, Nicolas Papadakis +1
The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson…
i-DEQ: A stable inertial deep equilibrium model for image restoration
Antonin Clerc, Marien Renaud, Baudouin Denis De Seneville +1
Deep Equilibrium Models (DEQs) are an established framework for image restoration that learn a problem-adapted regularization by solving a fixed-point (i.e. equilibrium) problem. W…
On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization
Guido Tapia-Riera, Camille Castera, Nicolas Papadakis
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent…
On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regu…
Optimization with First Order Algorithms
Charles Dossal, Samuel Hurault, Nicolas Papadakis
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The…