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- Hédy Attouch, Jérôme Bolte, Patrick Redont, Antoine Soubeyran
- Math. Oper. Res.
- 2010

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 : Rn → R∪{+∞} and g : Rm →… (More)

Given H a real Hilbert space and Φ : H → R a smooth C function, we study the dynamical system (DIN) ẍ(t) + αẋ(t) + β∇Φ(x(t))ẋ(t) +∇Φ(x(t)) = 0 where α and β are positive parameters. The inertial term… (More)

- Hédy Attouch, Zaki Chbani, Juan Peypouquet, Patrick Redont
- Math. Program.
- 2018

In a Hilbert space setting H, we study the fast convergence properties as t → +∞ of the trajectories of the second-order differential equation ẍ(t) + α t ẋ(t) +∇Φ(x(t)) = g(t), where ∇Φ is the… (More)

In a Hilbert space setting H, we study the fast convergence properties as t → +∞ of the trajectories of the second-order differential equation ẍ(t) + α t ẋ(t) +∇Φ(x(t)) = g(t), where ∇Φ is the… (More)

- Hédy Attouch, Patrick Redont, Antoine Soubeyran
- SIAM Journal on Optimization
- 2007

Given two objective functions f : X → R∪{+∞} and g : Y → R∪{+∞} on abstract spaces X and Y, and a coupling function c : X × Y → R+, we introduce and study alternative minimization algorithms of the… (More)

- Hédy Attouch, Juan Peypouquet, Patrick Redont
- SIAM Journal on Optimization
- 2014

Abstract. We introduce a new class of forward-backward algorithms for structured convex minimization problems in Hilbert spaces. Our approach relies on the time discretization of a second-order… (More)

We consider the second-order differential system with Hessian-driven damping ü+αu̇+β∇2Φ(u)u̇+∇Φ(u)+∇Ψ(u) = 0, where H is a real Hilbert space, Φ, Ψ : H → IR are scalar potentials, and α, β are… (More)

- Hédy Attouch, Patrick Redont, Benar Fux Svaiter
- J. Optimization Theory and Applications
- 2013

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of… (More)

We study the convergence properties of alternating proximal minimization algorithms for (nonconvex) functions of the following type: L(x, y) = f(x) + Q(x, y) + g(y) where f : R → R∪{+∞} and g : R →… (More)

We first study the fast minimization properties of the trajectories of the second-order evolution equation ẍ(t) + α t ẋ(t) + β∇Φ(x(t))ẋ(t) +∇Φ(x(t)) = 0, where Φ : H → R is a smooth convex function… (More)