This paper shows that error bounds can be used as effective tools for deriving complexity
results for first-order descent methods in convex minimization. In a first stage, this objective …

Nonconvex-concave min-max problem arises in many machine learning applications
including minimizing a pointwise maximum of a set of nonconvex functions and robust …

In a Hilbert space setting ℋ, given Φ: ℋ→ ℝ a convex continuously differentiable function,
and α a positive parameter, we consider the inertial dynamic system with Asymptotic …

In machine learning, models that generalize better often generate outputs that lie on a low-
dimensional manifold. Recently, several works have separately shown finite-time manifold …

In high dimensional regression settings, sparsity enforcing penalties have proved useful to
regularize the data-fitting term. A recently introduced technique called screening rules …

This thoroughly updated new edition presents state of the art sparse and multiscale image
and signal processing. It covers linear multiscale geometric transforms, such as wavelet …

Screening rules allow to early discard irrelevant variables from the optimization in Lasso
problems, or its derivatives, making solvers faster. In this paper, we propose new versions of …

In a Hilbert space \mathcalH, assuming (\alpha_k) a general sequence of nonnegative
numbers, we analyze the convergence properties of the inertial forward-backward algorithm …

In a Hilbert space HH, we study the convergence properties of a class of relaxed inertial
forward–backward algorithms. They aim to solve structured monotone inclusions of the form …

In a Hilbert space H, we study the asymptotic behavior, as time variable t goes to+∞, of
nonautonomous gradient-like inertial dynamics, with a time-dependent viscosity coefficient …