Publications related to Certification Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs

Universal and adaptive methods for robust stochastic optimization

Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

EPFL2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

Large Steps in Inverse Rendering of Geometry

Wenzel Alban Jakob, Baptiste Alexandre Marie Philippe Claude Nicolet

Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

ASSOC COMPUTING MACHINERY2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

Volkan Cevher, Ali Kavis

In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...

2021

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Tommaso Vanzan

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

Springer-Verlag2021

Forward-reflected-backward method with variance reduction

Volkan Cevher, Ahmet Alacaoglu

We propose a variance reduced algorithm for solving monotone variational inequalities. Without assuming strong monotonicity, cocoercivity, or boundedness of the domain, we prove almost sure convergence of the iterates generated by the algorithm to a soluti ...

2021

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

PERGAMON-ELSEVIER SCIENCE LTD2019

Certification Aspects of the Fast Gradient Method for Solving the Dual of Parametric Convex Programs

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Universal and adaptive methods for robust stochastic optimization

Localization errors of the stochastic heat equation

A combinatorial proof of a sumset conjecture of Furstenberg

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Large Steps in Inverse Rendering of Geometry

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Forward-reflected-backward method with variance reduction

Multi space reduced basis preconditioners for parametrized Stokes equations

Localization errors of the stochastic heat equation

A combinatorial proof of a sumset conjecture of Furstenberg

Universal and adaptive methods for robust stochastic optimization

Multi space reduced basis preconditioners for parametrized Stokes equations

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Large Steps in Inverse Rendering of Geometry

STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Forward-reflected-backward method with variance reduction