This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …

The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely
many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a …

We study the convergence properties of an alternating proximal minimization algorithm for
nonconvex structured functions of the type: L (x, y)= f (x)+ Q (x, y)+ g (y), where f and g are …

Regularized regression problems are ubiquitous in statistical modeling, signal processing,
and machine learning. Sparse regression, in particular, has been instrumental in scientific …

Many shape and image processing tools rely on computation of correspondences between
geometric domains. Efficient methods that stably extract" soft" matches in the presence of …

A number of recent works have emphasized the prominent role played by the Kurdyka-
Łojasiewicz inequality for proving the convergence of iterative algorithms solving possibly …

Classical federated learning (FL) enables training machine learning models without sharing
data for privacy preservation, but heterogeneous data characteristic degrades the …

Subsurface velocities within the Earth often contain piecewise-constant structures with sharp
interfaces. Acoustic-and elastic-waveform inversion (AEWI) usually produces smoothed …

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in
modern Machine Learning practice. Understanding the statistical fluctuations engendered …

Alternating Proximal Algorithms for Weakly Coupled Convex Minimization Problems.
Applications to Dynamical Games and PDE’s Page 1 Journal of Convex Analysis Volume …