Variable Bregman Majorization-Minimization algorithms for nonconvex nonsmooth optimization, with application to Poisson imaging
Abstract
In this work, we introduce a unifying Bregman-based majorization-minimization (MM) framework for solving nonconvex nonsmooth optimization problems. The proposed approach leverages Bregman divergences, possibly varying across iterations, to construct tailored surrogate functions that majorize the objective. We establish the convergence of the iterates of the resulting variable Bregman MM algorithm to critical points under the Kurdyka-Łojasiewicz property, relaxing standard assumptions such as the Lipschitz smoothness of the nonconvex objective function. We derive a constructive methodology to build a broad class of variable Bregman majorants with tractable minimizers. Our study encapsulates various existing majorization techniques, in particular those derived for Poisson data fidelity terms in imaging inverse problems. Numerical experiments on Positron Emission Tomography (PET) image reconstruction with a nonconvex regularizer showcase the practical feasibility of the proposed scheme.
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BibTeX
@article{adly2026variable,
title = {{Variable Bregman Majorization-Minimization algorithms for nonconvex nonsmooth optimization, with application to Poisson imaging}},
author = {Maxence Adly and Alix Chazottes and Émilie Chouzenoux and Jean-Christophe Pesquet and Florent Sureau},
journal = {SIAM Journal on Imaging Sciences},
year = {2026},
month = oct,
url = {https://inria.hal.science/hal-05589469v3},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Variable Bregman Majorization-Minimization algorithms for nonconvex nonsmooth optimization, with application to Poisson imaging
AU - Maxence Adly
AU - Alix Chazottes
AU - Émilie Chouzenoux
AU - Jean-Christophe Pesquet
AU - Florent Sureau
PY - 2026
DA - 2026/10/05
JO - SIAM Journal on Imaging Sciences
UR - https://inria.hal.science/hal-05589469v3
AB - In this work, we introduce a unifying Bregman-based majorization-minimization (MM) framework for solving nonconvex nonsmooth optimization problems. The proposed approach leverages Bregman divergences, possibly varying across iterations, to construct tailored surrogate functions that majorize the objective. We establish the convergence of the iterates of the resulting variable Bregman MM algorithm to critical points under the Kurdyka-Łojasiewicz property, relaxing standard assumptions such as the Lipschitz smoothness of the nonconvex objective function. We derive a constructive methodology to build a broad class of variable Bregman majorants with tractable minimizers. Our study encapsulates various existing majorization techniques, in particular those derived for Poisson data fidelity terms in imaging inverse problems. Numerical experiments on Positron Emission Tomography (PET) image reconstruction with a nonconvex regularizer showcase the practical feasibility of the proposed scheme.
SN - 1936-4954
ER -