286 citations · 522 across the 27 of their papers we have counts for
30 papers
Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption
Daniel Cortild, Mathias Staudigl, Juan Peypouquet +1
We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives. Existing stochastic extensions of dynamic barrier gradie…
Preconditioned primal-dual algorithms for saddle point problems: non-ergodic convergence rates
Huiyuan Guo, Juan José Maulén, Juan Peypouquet
We study a family of preconditioned primal dual algorithms for convex-concave saddle point problems by the dynamics introduced in \cite{apidopoulos2026preconditioned}. The proposed…
Inertial Primal Dual Dynamics with Hessian-driven Damping for Saddle Point Problems
Zepeng Wang, Juan Peypouquet
Featuring Hessian-driven damping, two inertial primal dual dynamical systems are proposed for solving smooth saddle point problems with bilinear coupling. For convex-concave functi…
Inertial forward-backward algorithm with exterior penalization and Tikhonov regularization
Siqi Qu, Juan Peypouquet, Mathias Staudigl
In a real Hilbertian setting, we develop in this paper numerical splitting techniques guaranteeing strong convergence to the least norm solution of constrained variational inequali…
Accelerated Backward Forward Method for Convex Optimization
Zepeng Wang, Juan Peypouquet
We analyze the convergence rate of an accelerated backward forward method for solving convex composite optimization problems. The method was developed by Taylor, Hendrickx and Glin…
Asymptotic behaviour of coupled random dynamical systems with multiscale aspects
D. Russell Luke, Johannes-Carl Schnebel, Mathias Staudigl +2
We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems cont…
Adaptive Accelerated Gradient Method for Smooth Convex Optimization
Zepeng Wang, Juan Peypouquet
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means…
Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Guillaume Garrigos, Daniel Cortild, Lucas Ketels +1
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question…
Fast convex optimization via inertial systems with asymptotically vanishing viscosity and Hessian-driven damping
Zepeng Wang, Juan Peypouquet
We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-d…
Convergence Rate Analysis for Monotone Accelerated Proximal Gradient Method
Zepeng Wang, Juan Peypouquet
We propose a monotone accelerated proximal gradient method for solving convex composite optimization problems, guaranteeing nonincreasing function values along the iterates -- a pr…
Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart
Juan José Maulén, Huiyuan Guo, Juan Peypouquet
We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the resta…
Preconditioned primal-dual dynamics in convex optimization: non-ergodic convergence rates
Vassilis Apidopoulos, Cesare Molinari, Juan Peypouquet +1
We introduce and analyze a continuous primal-dual dynamical system in the context of the minimization problem , where and are convex functions and is a line…
Bias-Optimal Bounds for SGD: A Computer-Aided Lyapunov Analysis
Daniel Cortild, Lucas Ketels, Juan Peypouquet +1
The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias com…
Asymptotic behavior of penalty dynamics for constrained variational inequalities
Siqi Qu, Mathias Staudigl, Juan Peypouquet
We propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dime…
A unified analysis on the speedup of accelerated gradient methods: An inertial dynamics approach
Zepeng Wang, Juan Peypouquet
Nesterov's Accelerated Gradient Method is one of the most popular first order optimization algorithms. When applied to -smooth, -strongly convex functions, it converges at a…
A Speed Restart Scheme for a Dynamical System with Hessian-Driven Damping and Three Constant Coefficients
Huiyuan Guo, Juan José Maulén, Juan Peypouquet
In this paper, we study a speed restart scheme for an inertial system with Hessian-driven damping. We establish a linear convergence rate for the function values along the restarte…
Global Optimization Algorithm through High-Resolution Sampling
Daniel Cortild, Claire Delplancke, Nadia Oudjane +1
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potentia…
Krasnoselskii-Mann Iterations: Inertia, Perturbations and Approximation
Daniel Cortild, Juan Peypouquet
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unifie…
A speed restart scheme for a dynamics with Hessian driven damping
Juan Jose Maulen, Juan Peypouquet
In this paper, we analyze a speed restarting scheme for the dynamical system given by whe…
Inertial Krasnoselskii-Mann Iterations
Juan José Maulén, Ignacio Fierro, Juan Peypouquet
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the n…
Forward-backward approximation of evolution equations in finite and infinite horizon
Andres Contreras, Juan Peypouquet
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequenc…
Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators
Hedy Attouch, Juan Peypouquet
We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator wit…
Fast convex optimization via inertial dynamics with Hessian driven damping
Hedy Attouch, Juan Peypouquet, Patrick Redont
We first study the fast minimization properties of the trajectories of the second-order evolution equation $$\ddot{x}(t) + \fracα{t} \dot{x}(t) + β\nabla^2 Φ(x(t))\dot{x} (t) + \na…
The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than
Hedy Attouch, Juan Peypouquet
The {\it forward-backward algorithm} is a powerful tool for solving optimization problems with a {\it additively separable} and {\it smooth} + {\it nonsmooth} structure. In the con…