Add to ORKGWe investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions on (proper, geodesic) Gromov hyperbolic spaces. We show that the proximal point algorithm from an arbitrary initial point can find a point close to a minimizer of the function. Moreover, we establish a contraction estimate for the proximal (resolvent) operator.Comment: 16 page
This paper proposes and develops inexact proximal methods for finding stationary points of the sum o...
This book aims to give an introduction to generalized derivative concepts useful in deriving necessa...
AbstractIn this paper, we show that the convex optimization problem can be solved by the proximal po...
We address composite optimization problems, which consist in minimizing thesum of a smooth and a mer...
First online: 24 February 2015We develop the theory of discrete-time gradient flows for convex funct...
We provide some counterexamples concerning the uniqueness and regularity of weak solutions to the in...
Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. He...
Abstract. We develop the theory of discrete-time gradient flows for convex func-tions on Alexandrov ...
For a natural class of discretisations of a convex domain in $R^n$, we consider the dynamical optim...
The Minimizing Movement (MM) scheme is a variational method introduced by E. De Giorgi to solve grad...
The proximal gradient and its variants is one of the most attractive first-order algorithm for minim...
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman...
We construct the fundamental solution of second order parabolic equations in non-divergence form und...
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical s...
The proximal point algorithm has known these last years many developments connected with the expansi...
This paper proposes and develops inexact proximal methods for finding stationary points of the sum o...
This book aims to give an introduction to generalized derivative concepts useful in deriving necessa...
AbstractIn this paper, we show that the convex optimization problem can be solved by the proximal po...
We address composite optimization problems, which consist in minimizing thesum of a smooth and a mer...
First online: 24 February 2015We develop the theory of discrete-time gradient flows for convex funct...
We provide some counterexamples concerning the uniqueness and regularity of weak solutions to the in...
Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. He...
Abstract. We develop the theory of discrete-time gradient flows for convex func-tions on Alexandrov ...
For a natural class of discretisations of a convex domain in $R^n$, we consider the dynamical optim...
The Minimizing Movement (MM) scheme is a variational method introduced by E. De Giorgi to solve grad...
The proximal gradient and its variants is one of the most attractive first-order algorithm for minim...
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman...
We construct the fundamental solution of second order parabolic equations in non-divergence form und...
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical s...
The proximal point algorithm has known these last years many developments connected with the expansi...
This paper proposes and develops inexact proximal methods for finding stationary points of the sum o...
This book aims to give an introduction to generalized derivative concepts useful in deriving necessa...
AbstractIn this paper, we show that the convex optimization problem can be solved by the proximal po...