About me
My research focuses on numerical optimization. I am interested in designing algorithms for nonsmooth optimization problems arising in sparse optimization and for non-convex problems, including mathematical programs with complementarity problems, bilevel optimization problems, and generalized Nash equilibrium problems.
Future plans
- May, 2023, JOpt 2023, HEC, Montreal, Canada;
- July, 2023, JuliaCon 2023, MIT, Boston, USA.
News
December 2022: PDENLPModels.jl published in JOSS
Published:
I am very happy to announce the publication in the Journal of Open Source Software of the paper PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints.
September 2022: A new package: FletcherPenaltySolver.jl
Published:
The package FletcherPenaltySolver.jl is now a Julia package !! Very happy about this one because it has been a long project and the solver with great for large problems. Besides, we always teach penalty methods at the University, but efficient implementations are scarce.
July 2022: JuliaSmoothOptimizers at the JuliaCon 2022
Published:
I showed how to use JuliaSmoothOptimizers framework to PDE-constrained optimization problems modeled with PDENLPModels.jl at this year’s JuliaCon 2022/JuMP-dev 2022. The conference featured three talks on JuliaSmoothOptimizers in the JuMP-dev stream.
June 2022: Closing the Winter Sessions
Published:
I taught in french the class MTH8408 Méthodes d’optimisation et contrôle optimal during the winter session at Polytechnique Montréal on numerical methods for optimization, variational calculus, and optimal control.
May 2022: Conference: JuliaSmoothOptimizers at Optimization Days Montréal
Published:
We organized a steam of sessions on ’’Numerical optimization and linear algebra with Julia’’ at Optimization Days/Journées de l’optimisation 2022 held at HEC Montréal, May 16-18, 2022. The conference, renowned for its optimization expertise and wine & cheese party, was held in-person for the first time since 2019!
February 2022: Talk on JuliaSmoothOptimizers and the NLPModel API
Published:
Yesterday was …. the 10th anniversary of Julia, and, yes, valentine’s day also. To celebrate this, we had the opportunity to present JuliaSmoothOptimizers at the JuMP-dev seminar and talk about the API for nonlinear models JuMP nonlinear developers call: The JuliaSmoothOptimizers ecosystem.
February 2022: DCISolver.jl published in JOSS
Published:
Last December, we submitted a paper to the Journal of Open Source Software related to the package DCISolver.jl
and it is now published!
January 2022: Partially differentiable projects
Published:
I am starting a new year in Montreal and one of the main projects for this year is to move forward in finalizing an ecosystem for optimization problems with partial differential equations in the constraints. The ecosystem is hosted under the JuliaSmoothOptimizers umbrella and contains:
- PDENLPModels.jl a package to model the PDE-constrained optimization problem using Gridap.jl Finite-Element discretization for the PDE.
- PDEOptimizationProblems contains a collection of 39 problems using PDENLPModels. It includes most of the problems from the COPS test set.
November 2021: A new package: RandomLinearAlgebraSolvers.jl
Published:
The package RandomLinearAlgebraSolvers.jl is now a Julia package. It contains randomized iterative methods for linear algebra and random projectors used to solve linear systems in the sense of the Johnson–Lindenstrauss lemma. The package is still at an early stage and new contributions are very welcome. You will find below an example extracted from the package’s documentation. The package uses Stopping.jl as a framework for iterative methods.
October 2021: IVADO, Digital October
Published:
As part of my postdoc at IVADO, I presented my work on solving PDE-constrained optimization problems in Julia during IVADO’s annual conference, IVADO Digital October. It was a 3min presentation, and a great challenge for such challenging problem! The video is now available on Youtube, and, as usual, more on the various packages on GitHub @tmigot.
Winter 2021: News and Publications
Published:
Some news following our work in Guelph with an article on the website of the CEPS Guelph presenting some nice applications of GNEPs.
New Position in Montréal
Published:
I am starting a new postdoc position in Polytechnique Montréal with Dominique Orban on solvers for optimization problems involving PDE constraints in Julia and data science applications. This new position is funded by a competitive grant of IVADO, the institute for data valorization in Montreal.
Summer 2020: Publications
Published:
Two publications have been accepted this summer: On approximate stationary points of the regularized mathematical program with complementarity constraints in JOTA and The new butterfly relaxation method for mathematical programs with complementarity constraints in the proceedings of the Indo-French seminar. These works are the theoretical basis toward the computation of M-stationary points of the MPCC. I also continue to update the Julia:
- MPCC.jl Set of tools to model the mathematical program with complementarity/switching/vanishing constraints following the NLPModels structure and with basic tools to use the Stopping framework.
- MPCCSolver.jl A set of algorithms to solve the models from MPCC.jl.
I also had the pleasure to present A differential inclusion approach to mineral precipitation-dissolution reactions in geochemistry in collaboration with Jocelyne Erhel and Bastien Hamlat in the online Workshop Variational Methods in Nonlinear Phenomena. This work is part of Bastien’s Ph.D. thesis that he successfully defended this month, Congrats!!!
Conference in Toronto [Update]
Published:
The workshop has now evolved as an online workshop to maintain active researches despite the current pandemic, see the schedule here!
Winter 2020: Seminars and a publication
Published:
To celebrate the new year, I gave in January a seminar talk at the Departmental Colloquium Series in Guelph where I motivated the GNEP and presented some of our findings with Monica Cojocaru. In particular, it was based on this new paper we got accepted A dynamical system approach to the generalized Nash equilibrium problem in the open access Journal of Nonlinear and Variational Analysis. The paper reviews the use of nonsmooth dynamical system to find generalized Nash equilibria.
Stopping v.0.2
Published:
The new version of Stopping.jl is now official on Julia. It is the first stable version of it, and I will now soon release more codes using it for MPCC and GNEP. Currently, the main page of the project is here: Stopping.jl
Fall 2019: Publications
Published:
I taught a new course in Guelph this Fall, and in the meantime, 3 papers have been accepted.
Summer 19: Talks
Published:
I gave a couple of talks over the summer at the EURO conference 2019 EURO conference, Dublin, Ireland (and co-organize a stream on games with 18 talks!), the 2019 World Congress on Global Optimization, Metz, France, the 2019 ICCOPT, Berlin, Germany, the MOPTA 2019, Lehigh, USA and finally the AMMCS-2019, Waterloo, Ontario (co-organize of a special session on optimization). Now, back in Guelph for a second year and teach a new class this Fall.
Stopping v.0.1
Published:
I gave a talk entitled “Stopping.jl: A framework to implement iterative optimization algorithms” in the Journées de l’optimisation 2019, Montréal, Québec in the session Optimization in Julia to introduce our new Julia package.
Winter 19: Publications and a new preprint
Published:
This winter, I’m teaching a fun course in Guelph. In the meantime, several papers have been accepted for publication.
Conference
Published:
I gave a talk on the KKT conditions of the GNEP during the 2018 CMS Winter Meeting in Vancouver.
New Position in Guelph
Published:
I started a 2 years post-doc position in Guelph under the supervision of Monica Cojocaru. I will work on bringing optimization methods for Generalized Nash Equilibrium Problems.
New Position in Sherbrooke
Published:
I am back in Sherbrooke for three months after winning a grant in the interdisciplinary program “Programme de bourses d’excellence pour étudiants étrangers” of FRQNT. I will continue working on a solver for degenerate non-linear programs in Julia in collaboration with Jean-Pierre Dussault.
Spring 18: Talks
Published:
I attended two conferences this spring from May, 2nd to 4th LOPAL in Rabat (Marocco) and from June 3rd to 6th in Castro Urdiales, Spain.
New Position in INRIA
Published:
I join the team FLUMINANCE at INRIA Rennes for a few months to work on dynamical complementarity problems with Jocelyne Erhel.
PhD Defense
Published:
I have successfully defended my PhD thesis in Rennes. You can find the slides here and the manuscript here.
Conference
Published:
I gave a talk on regularization methods for MPCC and its extension to MPVC in ParaoptXI (19-22 september) in Prague. UPDATE: you can now find a preprint on this subject here. UPDATE 2: The paper is published in Optimization (doi:10.1080/02331934.2018.1542531)
Preprint
Published:
I posted on HAL a work in collaboration with Jean-Pierre Dussault, Mounir Haddou, and Abdeslam Kadrani on relaxation methods for mathematical programs with complementarity constraints and the approximate resolution of their sub-problems entitled : How to Compute a Local Minimum of the MPCC. I will present part of this work during the conference EUROPT 2017 in Montréal.
Preprint
Published:
I posted on HAL a work on the butterfly relaxation method for mathematical programs with complementarity constraints in collaboration with Jean-Pierre Dussault and Mounir Haddou entitled: The New Butterfly Relaxation Methods for Mathematical Programs with Complementarity Constraints.
Talk INFORMS
Published:
I gave a talk about the butterfly relaxation method for mathematical programs with complementarity constraints at the INFORMS 2016 Annual Meeting, which were organized in the city of music Nashville (Tennessee, US) from 14 to 16 of November 2016, see the slides.
Conference in Rennes
Published:
I was in the organizing committee of the conference HJ2016: Hamilton-Jacobi Equations: new trends and applications, which takes place from 30 May to 3 June 2016 in Rennes (France). I also presented there a poster on: “A new relaxation method for the mathematical program with complementarity constraints.”
Talk and publication
Published:
I gave a talk about interior point methods for monotone linear complementarity problems at the Journées SMAI-MODE 2016, which were organized in Toulouse from 23 to 25 of March 2016, see the slides. You can find a preprint of this work on HAL. UPDATE Jan. 2018: the paper has been accepted in Optimization Letters (doi: 10.1007/s11590-018-1241-2).
Publication
Published:
I posted on HAL a work on a numerical method for the absolute value equation in collaboration with Lina Abdallah from Tripoli, Lebanon, and Mounir Haddou entitled: Solving Absolute Value Equation using Complementarity and Smoothing Functions. EDIT: The paper has been accepted in Journal of Computational and Applied Mathematics (doi :10.1016/j.cam.2017.06.019).