Fast convex optimization via inertial dynamics with Hessian driven damping

Autor: Attouch, Hedy, Peypouquet, Juan, Redont, Patrick

We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \beta \nabla^2 \Phi (x(t))\dot{x} (t) + \nabla \Phi (x(t)) = 0,$$ where $\Phi:\mathcal H\to\mathb

Externí odkaz: http://arxiv.org/abs/1601.07113

Proximal alternating minimization and projection methods for nonconvex problems. An approach based on the Kurdyka-Lojasiewicz inequality

Autor: Attouch, Hedy, Bolte, Jerome, Redont, Patrick, Soubeyran, Antoine

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 $f:\R^n\rightarrow\R\cup{+\infty}$ and $g:\R^m\rightarrow\R\cup{+\infty}$ are prope

Externí odkaz: http://arxiv.org/abs/0801.1780

Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality

Autor: Attouch, Hédy, Bolte, Jérôme, Redont, Patrick, Soubeyran, Antoine

Publikováno v: Mathematics of Operations Research, 2010 May 01. 35(2), 438-457.

Externí odkaz: https://www.jstor.org/stable/40801236

Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity.

Autor: Attouch, Hedy¹, Redont, Patrick¹, Chbani, Zaki², Peypouquet, Juan³

Publikováno v: Mathematical Programming. Mar2018, Vol. 168 Issue 1/2, p123-175. 53p.

Alternating minimization and projection methods for structured nonconvex problems

Autor: Attouch, Hedy, Bolte, Jérôme, Redont, Patrick, Soubeyran, Antoine

Publikováno v: Mathematics of Operations Research
Mathematics of Operations Research, 2010, 35 (2), pp.438-457. ⟨10.1287/moor.1100.0449⟩
Mathematics of Operations Research, INFORMS, 2010, 35 (2), pp.438-457. ⟨10.1287/moor.1100.0449⟩

International audience; 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 proper lower semicontinuous functions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::0b1a7f040fcd4298d5ed76474b787042
https://hal.science/hal-00803857