Publications associées à Méthode de Newton

General and Unified Model of the Power Flow Problem in Multiterminal AC/DC Networks

This paper proposes a generic and unified model of the power flow (PF) problem for multiterminal hybrid AC/DC networks. The proposed model is an extension of the standard AC-PF. The DC network is treated as an AC one and, in addition to the Slack, PV and P ...

IEEE Institute of Electrical and Electronics Engineers2024

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

EPFL2024

Scalable constrained optimization

Maria-Luiza Vladarean

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations

Giancarlo Ferrari Trecate, Maryam Kamgarpour, Yuning Jiang, Baiwei Guo

We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optim ...

IEEE2023

Tensor approximation of the self-diffusion matrix of tagged particle processes

Christoph Max Strössner

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Geometrically-Conditioned Point Diffusion Models

Pascal Fua, Eduard Trulls Fortuny, Michal Jan Tyszkiewicz

Diffusion models generating images conditionally on text, such as Dall-E 2 [51] and Stable Diffusion[53], have recently made a splash far beyond the computer vision com- munity. Here, we tackle the related problem of generating point clouds, both unconditi ...

2023

Technology Mapping Using Multi-output Library Cells

Giovanni De Micheli, Alessandro Tempia Calvino

Technology mapping transforms a technology-independent representation into a technology-dependent one given a library of cells. Even if technology libraries contain multi-output cells, state-of-the-art techniques fully exploit single-output cells only. Mul ...

2023

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Tobias Schneider, Jeremy Peter Parker

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

Cambridge University Press2022

Characterization and prediction of peptide structures on inorganic surfaces

Dmitrii Maksimov

Interfaces between peptides and metallic surfaces are the subject of great interest for possible use in technological and medicinal applications, mainly since organic systems present an extensive range of functionalities, are abundant, cheap, and exhibit l ...

EPFL2022

On the Double Descent of Random Features Models Trained with SGD

Volkan Cevher, Fanghui Liu

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/overparameterized regime. In this work, we derive precise non-asymptotic error bounds of RF regression under b ...

2022

Scalable Fabrication and Actuation of a Human Inspired Hand Through 3D Printed Flexures and Combinatorial Actuation

Josephine Anna Eleanor Hughes, Kai Christian Junge, Carlo Bosio

The fabrication and control of robot hands with biologically inspired structure remains challenging due to its cost and complexity. In this paper we explore how widely available FDM printers can be used to fabricate complex hand structures by leveraging co ...

FRONTIERS MEDIA SA2022

Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates

Nicolas Boumal

Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, ...

MICROTOME PUBLISHING2021

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

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

Optimization Methods for Control: From Embedded Programmable Hardware to Data-Driven Process Optimization

Harsh Ambarishkumar Shukla

The research community has been making significant progress in hardware implementation, numerical computing and algorithm development for optimization-based control. However, there are two key challenges that still have to be overcome for optimization-base ...

EPFL2021

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

Jochen Peter Hinz

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle ...

2021

A Newton Frank-Wolfe method for constrained self-concordant minimization

Volkan Cevher, Quoc Tran Dinh

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

SPRINGER2022

Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

Ali H. Sayed, Kun Yuan, Sulaiman A S A E Alghunaim

This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framewor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

A first-order primal-dual method with adaptivity to local smoothness

Volkan Cevher, Maria-Luiza Vladarean

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

Substructured Two-grid and Multi-grid Domain Decomposition Methods

Tommaso Vanzan

Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...

2022