Tangi Migot

Tangi Migot

Computational Scientist

Looking Back at the Winter Session

4 minute read

Published:

In the world of numerical optimization, the quest for efficiency, accuracy, and innovation never ceases. At Polytechnique Montréal, students embarking on their educational journey have a unique opportunity to explore this dynamic field through the course MTH8408 Méthodes d’optimisation et contrôle optimal. This course, which I had the privilege of teaching during the winter session of 2023, delves into the depths of numerical methods for optimization, variational calculus, and optimal control.

Teaching the same course in 2022 provided valuable insights that led to improvements, making the 2023 edition an even more enriching experience. The heart of MTH8408 lies in bridging theory and practice, giving students a well-rounded understanding of optimization. Here, we will take you on a journey through the course, its laboratory sessions, student projects, and the role of the powerful Julia programming language.

Course Overview

MTH8408 is a 36-hour course that equips students with a deep understanding of optimization algorithms, spanning various classes of problems. The primary objective is to ensure that students grasp the core concepts of optimization while gaining hands-on experience. It’s this unique blend of theory and practice that sets the course apart.

One remarkable aspect of the course is the extensive in-class discussions that dissect algorithms, focusing on the intricate details that render them efficient. A prime example is the utilization of matrix-free implementations for some algorithms. Such attention to detail ensures that students not only understand the algorithms but can also implement them effectively.

Laboratory Sessions

In addition to the classroom sessions, students spend 18 hours in the laboratory. Here, they get to grips with the Julia programming language, known for its power and flexibility in the field of scientific computing. More importantly, students have the opportunity to contribute to existing Julia packages, such as OptimizationProblems.jl.

The course uses several Julia packages:

What’s truly impressive is how quickly students adapt to Julia and these packages. In just a few hours, they are able to code a range of algorithms for unconstrained and equality-constrained optimization problems, as well as linear and nonlinear least squares problems. It’s a testament to both the students’ capabilities and the accessibility of Julia as a programming language.

Student Projects

One of the highlights of MTH8408 is the student projects. These projects allow students to explore areas of interest within the realm of optimization and apply their newfound knowledge and skills. The results from these projects are nothing short of astounding, often reaching the level of numerical results expected in research papers.

Some of the topics that students tackled in 2023 included parameter identification in financial market models, Gaussian process regression, quasi-Newton methods, first-order objective-function-free optimization algorithms, local solutions of the optimal power flow problem, nonsmooth R2 algorithms with constraints, and hybrid methods for nonlinear least squares.

The diversity of these projects demonstrates the breadth of optimization’s applications and the depth of the knowledge acquired during the course. Students are not just learning theory; they are actively contributing to the advancement of optimization research.

Teaching with Julia

Teaching MTH8408 using Julia and its associated packages has been a revelation. The simplicity and efficiency of Julia make it a powerful tool for teaching optimization. However, what truly makes a difference is the usage of a straightforward yet highly effective API, known as NLPModels, along with refined ideas and subsolvers for algorithms.

The students’ ability to implement algorithms and achieve exceptional results is a testament to both their aptitude and the efficacy of these tools. Julia has undoubtedly earned its place in the optimization classroom.

Personal Insights

Teaching MTH8408 is not just a professional endeavor; it’s a source of personal fulfillment. The interaction with students, their enthusiasm, and their achievements are incredibly rewarding. Moreover, teaching this course is a two-way street. It guides my research and helps me understand what truly matters in the world of numerical optimization. The students’ exploration of diverse projects continually expands my horizons and enriches my research endeavors.

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Presenting at JuMP-dev 2024 and Publishing in JuliaCon 2023 Proceedings

3 minute read

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I’m thrilled to share two major milestones in my recent work within the Julia ecosystem. First, I presented the latest developments in optimization solvers at JuMP-dev 2024, and second, my paper on JSOSuite.jl was accepted in The Proceedings of the JuliaCon Conferences.

These two achievements highlight both the ongoing evolution of JuliaSmoothOptimizers (JSO) and its growing impact on large-scale nonlinear optimization problems.

JuMP-dev 2024: Advancing Nonlinear Optimization with JuliaSmoothOptimizers

This year’s JuMP-dev workshop, held independently from JuliaCon for the first time in Montreal, offered a focused platform for deep dives into JuMP and its surrounding tools. In my presentation, I discussed the latest progress within the JuliaSmoothOptimizers (JSO) ecosystem, my slides and the replay.

At the core of my talk was an introduction to new solvers and packages like AdaptiveRegularization.jl, which address the unique challenges of large-scale optimization problems with Adaptive Regularization with Cubics. I emphasized the following key innovations:

  • Automatic Differentiation (AD) support and integration with JuMP for easier problem modeling.
  • Memory pre-allocation for in-place solvers, reducing runtime overhead.
  • Support for multi-precision solvers and GPU-based computations, essential for modern large-scale applications.
  • The value of factorization-free solvers, which excel in tackling large, complex problems, such as those in discretized PDE-constrained optimization.

For newcomers to JSO, JSOSuite.jl serves as a critical entry point, simplifying solver selection and benchmarking through automatic algorithm matching. This tool eliminates the complexity of choosing from multiple solvers by providing a user-friendly interface that adapts to the problem at hand. My talk also touched on the broader adoption and longevity of JSO, which now spans over 50 registered packages, making it one of the most comprehensive platforms for numerical optimization.

JuliaCon 2023: JSOSuite.jl – Simplifying Continuous Optimization

While JuMP-dev 2024 focused on recent developments, my publication in The Proceedings of the JuliaCon Conferences looks at the core philosophy and implementation behind JSOSuite.jl. Titled JSOSuite.jl: Solving Continuous Optimization Problems with JuliaSmoothOptimizers, the paper introduces JSOSuite.jl as a package designed to bring ease-of-use to complex optimization challenges.

JSOSuite.jl covers a range of problem types—from unconstrained to generally-constrained and least-squares problems—and eliminates the need for users to understand the intricate details of individual solvers. Instead, the package conducts a preliminary analysis of the problem and automatically selects the most appropriate solver, offering significant advantages to both experienced practitioners and newcomers alike.

This paper builds on the innovations within JSO, reinforcing its versatility and ease of use across various fields and applications. The package is a natural fit for researchers who need efficient, reliable solvers without the overhead of manually configuring them for different problem types.

Looking Forward

Both my presentation at JuMP-dev 2024 and the publication of the JSOSuite.jl paper reflect the significant strides made by the JuliaSmoothOptimizers organization over the past year. The JSO ecosystem is positioned to continue driving innovation in the field of numerical optimization.

I’m excited to see how these advancements will be applied across diverse optimization problems in the coming years and look forward to continuing this journey with the JSO community.

New Preprint on HAL: Exploring Projected Dynamical Systems in Geochemical Reactions

2 minute read

Published:

This project holds a special place in my heart as it touches on the very applications in geochemistry that first drew me into research. Equilibrium reactions, particularly in slow processes like the water cycle in aquifers, have always fascinated me. Moreover, this paper represents an important milestone for one of the authors, Bastien, as it was part of his Ph.D. thesis. The use of projected dynamical systems, a model I am particularly fond of, adds an additional layer of personal significance to this work.