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Concept

Fermat's theorem (stationary points)

Related publications (20)

Dynamical system approach to navigation around obstacles

Aude Billard, Aradhana Nayak

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

2024

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Mehmet Fatih Sahin

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

EPFL2023

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Baiwei Guo

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Patrick Thiran, Negar Kiyavash, Saber Salehkaleybar

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022

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

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...

IEEE2020

A Catalyst Framework for Minimax Optimization

Negar Kiyavash

We introduce a generic two-loop scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated dual problem and takes full advantage of existing ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2020

Second-Order Guarantees In Federated Learning

Ali H. Sayed, Stefan Vlaski, Elsa Rizk

Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally giv ...

IEEE2020

An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints

Volkan Cevher, Ahmet Alacaoglu, Fabian Ricardo Latorre Gomez, Armin Eftekhari, Mehmet Fatih Sahin

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to t ...

2019

Test and lower bound modeling of keyed shear connections in RC shear walls

Aurelio Muttoni, Jesper Harrild Sorensen

This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests sho ...

Engineering Structures2018

Low rank differential equations for Hamiltonian matrix nearness problems

Daniel Kressner

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axi ...

Springer2015

Reduced basis multiscale finite element methods for elliptic problems

Jan Sickmann Hesthaven

In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory ...

Society for Industrial and Applied Mathematics2015

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxima ...

2013

Portfolio construction under information asymmetry

Lionel Coulot

We introduce in this thesis the idea of a variable lookback model, i.e., a model whose predictions are based on a variable portion of the information set. We verify the intuition of this model in the context of experimental finance. We also propose a novel ...

EPFL2013

The effect of tissue geometry on the activation recovery interval of atrial myocytes

Vincent Jacquemet

The propagation of electric activity inside a realistically-shaped, thick-walled model of the atria was studied. The membrane kinetics was based on the formulations of Courtemanche, Ramirez and Nattel. In spite of the assumed uniformity of all kinetics par ...

2009

A Class Of Mean Field Interaction Models for Computer and Communication Systems

Jean-Yves Le Boudec

We consider models of N interacting objects, where the interaction is via a common resource and the distribution of states of all objects. We introduce the key scaling concept of intensity; informally, the expected number of transitions per object per time ...

2008

On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws

Erik Burman

A finite element method for Burgers' equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we a ...

Springer Netherlands2007

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Propriétés hors-équilibre d'une paroi adiabatique

Séverine Pache

We study the evolution of a system composed of N non-interacting particles of mass m distributed in a cylinder of length L. The cylinder is separated into two parts by an adiabatic piston of a mass M ≫ m. The length of the cylinder is a fix paramete ...

EPFL2004

Related publications (20)

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022