Stochastic differential equations for modeling first order optimization methods

Convex programming (90C25) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Ordinary differential equations and systems with randomness (34F05) Representations of entire functions of one complex variable by series and integrals (30D10)

Cites Work

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On semi- and subanalytic geometry
From error bounds to the complexity of first-order descent methods for convex functions
Inertial forward-backward algorithms with perturbations: application to Tikhonov regularization
Convergence rates of an inertial gradient descent algorithm under growth and flatness conditions
Understanding the acceleration phenomenon via high-resolution differential equations
Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
Convergence of the forward-backward algorithm: beyond the worst-case with the help of geometry
A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
An Introduction to Computational Stochastic PDEs
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
Convergence Rates of Damped Inertial Dynamics under Geometric Conditions and Perturbations
Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
On the long time behavior of second order differential equations with asymptotically small dissipation
On the Convergence of Gradient-Like Flows with Noisy Gradient Input
Optimization Methods for Large-Scale Machine Learning
Optimal Convergence Rates for Nesterov Acceleration
The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
Some methods of speeding up the convergence of iteration methods
Stochastic differential equations. An introduction with applications.

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