Concept

Steffensen's method

Related publications (11)

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 ...

2023

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Stochastic Composite Least-Squares Regression with Convergence Rate O(1/n)

Nicolas Henri Bernard Flammarion

We consider the minimization of a function deﬁned on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...

2017

Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams

Nikolaos Geroliminis, Mehmet Yildirimoglu

Real-time coordinated traffic management strategies that benefit from parsimonious models with aggregated network dynamics, provide a new generation of smart hierarchical strategies to improve network capacity and performance. However, this raises the ques ...

Elsevier2014

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulatio ...

Biomed Central Ltd2012

A multi-iterate method to solve systems of nonlinear equations

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Frank Crittin

We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...

2007

Numerical methods and models relevant to transportation applications

Michaël Clément Louis Ghislain Thémans

In this thesis, we focus on standard classes of problems in numerical optimization: unconstrained nonlinear optimization as well as systems of nonlinear equations. More precisely, we consider two types of unconstrained nonlinear optimization problems. On t ...

EPFL2007

A multi-iterate method to solve systems of nonlinear equations

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Frank Crittin

2006

Solving noisy large scale fixed point problems and systems of nonlinear equations

Michel Bierlaire, Frank Crittin

Many complex transportation models can be formulated as fixed-point problems. Typical examples are the equilibrium-like models, motivated by the need to capture the interaction between the transport supply (that is, the infrastructure) and transport demand ...

2006

Solving the anticipatory route guidance generation problem using a generalization of secant methods

Michel Bierlaire, Frank Crittin

Route guidance refers to information provided to travelers in an attempt to facilitate their decisions relative to departure time, travel mode and route. We are specifically interested in consistent anticipatory route guidance, in which real-time traffic m ...

2004

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