Publications associées à Méthode de la sécante

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Geometry-Driven Stock-Constrained Truss Design via Equilibrium-Based Structural Models

Corentin Jean Dominique Fivet, Tao Sun

This paper presents a geometry-driven approach to form-finding with reused stock elements. Our proposed workflow uses a K-mean algorithm to cluster stock elements and incorporate their geometrical values early in the form-finding process. A feedback loop i ...

Springer2024

Gyrokinetic simulations of turbulence and zonal flows driven by steep profile gradients using a delta-f approach with an evolving background Maxwellian

Laurent Villard, Stephan Brunner, Moahan Murugappan, Alberto Bottino, Ben McMillan

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulati ...

2022

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Tommaso Vanzan

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

2022

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

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

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

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Smooth Power Direction Transition of a Bidirectional LLC Resonant Converter for DC Transformer Applications

Drazen Dujic, Jakub Kucka

The bidirectional LLC resonant converter operated at fixed switching frequency is a preferable candidate for a true dc transformer that does not actively control the power flow. This is due to its naturally stiff voltage ratio regardless of the imposed loa ...

2020

Rapid Analysis of Arbitrary-Shaped Conformal Beam-Scanning Arrays

Anja Skrivervik, Denys Nikolayev

Conformal antenna arrays are able to fit seamlessly on curved 3D-shaped surfaces, which are found ubiquitously on vehicles, aircraft, a human body, etc. In addition, conformal structures can overcome the scan loss limitations of conventional planar arrays. ...

IEEE2020

Let’s be honest: An optimal no-regret framework for zero-sum games

Volkan Cevher, Mehmet Fatih Sahin, Ya-Ping Hsieh, Ehsan Asadi Kangarshahi

We revisit the problem of solving two-player zero- sum games in the decentralized setting. We pro- pose a simple algorithmic framework that simulta- neously achieves the best rates for honest regret as well as adversarial regret, and in addition resolves t ...

2018

Variational Methods for Human Modeling

Timur Bagautdinov

A large part of computer vision research is devoted to building models and algorithms aimed at understanding human appearance and behaviour from images and videos. Ultimately, we want to build automated systems that are at least as capable as people when i ...

EPFL2018

Quasi-Newton Methods for Real-Time Simulation of Hyperelastic Materials

Ladislav Kavan, Sofien Bouaziz

We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position-Based or Projective Dynamics are fast but support only a limited selection of materials; even classi ...

2017

Distributed Modifier-Adaptation Schemes for the Real-Time Optimization of Interconnected Systems in the Presence of Structural Plant-Model Mismatch

Dominique Bonvin, René Uwe Schneider, Predrag Milosavljevic

The desire to operate chemical processes in a safe and economically optimal way has motivated the development of so-called real-time optimization (RTO) methods [1]. For continuous processes, these methods aim to compute safe and optimal steady-state set ...

2016

Large-scale extraction of brain connectivity from the neuroscientific literature

Jean-Cédric Chappelier, Sean Lewis Hill, Martin Telefont, Renaud Luc Richardet

In neuroscience, as in many other scientific domains, the primary form of knowledge dissemination is through published articles. One challenge for modern neuroinformatics is finding methods to make the knowledge from the tremendous backlog of publications ...

Oxford Univ Press2015

An Augmented Lagrangian Coordination-Decomposition Algorithm for Solving Distributed Non-Convex Programs

Colin Neil Jones, Jean-Hubert Hours

A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a standard multiplier m ...

2014

A two-level time step technique for the partitioned solution of one-dimensional arterial networks

Simone Deparis, Adelmo Cristiano Innocenza Malossi

In this work a numerical strategy to address the solution of the blood flow in one-dimensional arterial networks through a topology-based decomposition is presented. Such decomposition results in the local analysis of the blood flow in simple arterial segm ...

Elsevier2012

Direct data-driven H2 − H∞ loop-shaping

Alireza Karimi

In this paper, a direct data-driven approach is proposed to tune fixed-order controllers for unknown stable LTI plants in a mixed-sensitivity loop-shaping problem. The method requires a single set of input-output samples and it is based on simple convex op ...

2011

A Recursive Acceleration Technique for Static Potential Green's Functions of a Rectangular Cavity Combining Image and Modal Series

Juan Ramon Mosig, Michael Mattes, Sergio Lopez Pena

A hybrid acceleration algorithm for the computation of the static potential Green’s functions of a rectangular cavity is proposed. Similarly to Ewald’s method, it combines the series expansions in terms of images and modes. The main particularity with resp ...

Institute of Electrical and Electronics Engineers2011