arXiv subjects

Mathieu Besançon

Publications and source records attributed to Mathieu Besançon.

40 records · Page 3Linked to original sources

arXiv2021

FrankWolfe.jl: a high-performance and flexible toolbox for Frank-Wolfe algorithms and Conditional Gradients

We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and Conditional Gradients variants for first-order constrained optimization. The package is designed with flexibility and high-performance in mind, allowing for easy extension and relying on few assumptions regarding the user-provided functions. It supports Julia's unique multiple dispatch feature, and interfaces smoothly with generic linear optimization formulations using MathOptInterface.jl.

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arXiv2021

Distributions.jl: Definition and Modeling of Probability Distributions in the JuliaStats Ecosystem

Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features for their intuitive and flexible manipulation, while remaining highly efficient through zero-cost abstractions.

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arXiv2020

Complexity of near-optimal robust versions of multilevel optimization problems

Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.

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arXiv2019

A Bilevel Approach to Optimal Price-Setting of Time-and-Level-of-Use Tariffs

Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this self-determined capacity limit. We introduce a variant of the TLOU defined in the literature, aligned with the supplier interest to prevent unplanned over-consumption. The optimal price-setting problem of TLOU is defined as a bilevel, bi-objective problem anticipating user choices in the supplier decision. An efficient resolution scheme is developed, based on the specific discrete structure of the lower-level user problem. Computational experiments using consumption distributions estimated from historical data illustrate the effectiveness of the proposed framework.

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