Antoine Lesage-Landry

christina.soldati@mila.quebec

Christina G. Soldati

PhD - Polytechnique Montréal

Noureddine Toumi Toumi

Postdoctorate - Polytechnique Montréal

toumi.noureddine@gmail.com

Etienne Tremblay

PhD - Polytechnique Montréal

etienne.tremblay@mila.quebec

Theodoros Xenakis

Research Intern - Polytechnique Montréal

theodoros.xenakis@mila.quebec

Website

maeva-cybelle.zambou-zoleko@mila.quebec

Chao Yin

PhD - Polytechnique Montréal

chao.yin@polymtl.ca

Maeva Zambou Zoleko

PhD - Polytechnique Montréal

william.zhang@mila.quebec

William Zhang

Master's Research - Polytechnique Montréal

Website

Publications

Optimal energy trading in residential prosumer clusters via graphon mean field games

Mohamad Aziz

Hussein Suprême

Hanane Dagdougui

2026-07-13

Electric Power Systems Research (published)

Copositive Characterizations of Convex Hull Pricing

Madhusudan Ghosh

Joshua Adam Taylor

Due to the nonconvex binary constraints of unit commitment (UC), no uniform linear pricing scheme supports the optimal dispatch. Convex hull… (see more) pricing (CHP) and copositive duality pricing (CDP) both address this problem. CHP derives the price from the subgradient of the value function of the convex hull relaxation of UC. CDP refers to several different pricing mechanisms that can be constructed from the dual multipliers of the completely positive programming reformulation. In this work, we define a centralized convex hull price over the joint feasible set of UC and prove that, under non-degeneracy, it coincides with the marginal copositive duality price. Numerical experiments on the Scarf example validate this equivalence and quantify the pricing gap introduced by the semidefinite restriction.

2026-07-12

arXiv (preprint)

Parallel versions of the mesh adaptive direct search algorithm

Sébastien Le Digabel

Samuel Mendoza

Christophe Tribes

This work surveys the different parallel variants of the mesh adaptive direct search (MADS) algorithm for constrained blackbox optimization.… (see more) These problems can inherently imply high computational costs due to the possible large number of variables and multi-modality of the search space. In addition, the potential time-intensive nature and time heterogeneity of the blackboxes defining the problem prompts the need for efficient implementations. Parallelism emerges as an actionable solution to mitigate computation time, as modern computer systems rely on multi-core architecture. The reviewed methods employ diverse levels of parallelism and distinct parallel strategies to effectively tackle each aspect outlined above. The manuscript details the practical implementations, provides computational results, and offers insights into the advantages and limitations of each MADS parallel method.

2026-07-08

arXiv (preprint)

Convex training of Lipschitz-regularized shallow neural networks

Chao Yin

In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks. We solve a… (see more) non-convex Lipschitz-regularized training program by introducing a convex restriction that can be efficiently solved to global optimality. Our approach can be employed as a post-processing step by taking a pre-trained network as an initial solution to then solving the convex program whose optimal network is guaranteed to be no worse than the initial one. We illustrate the improvements of our training procedure with experiments using real world datasets for regression tasks under an adversarial setting. We show numerically that solving our proposed convex program yields networks with lower objective values on the Lipschitz-regularized program compared to existing methods. Additionally, we show that on certain datasets, networks obtained using our convex training program are both more accurate and robust with respect to adversarial attacks.

2026-06-16

arXiv (preprint)

Online Sketched Newton-Raphson

Jean-Luc Lupien

Yuen-Man Pun

Youssef Diouane

Iman Shames

In online convex optimization (OCO), a decision-maker is confronted with an unknown environment and seeks to play an optimal sequence of dec… (see more)isions on a short time-scale using only past information. Recent advances in second-order OCO methods have demonstrated tighter regret bounds and improved empirical performance over traditional first-order methods. However, this performance comes at a cost: a matrix inversion is now required, which scales with the cube of the size of the problem. In this work, we propose sketching to mitigate this limitation. Specifically, we present the online sketched Newton-Raphson method (OSNR) which preserves the tight regret bounds obtained with second-order methods while presenting a strict computational improvement in terms of complexity. We discuss three application scenarios of OSNR: online root finding, unconstrained OCO, and time-varying equality-constrained OCO, and present their respective regret and a constraint violation bound for the latter. In all three applications, OSNR achieves sublinear dynamic regret bounds. For the equality-constrained case, the extension OSNR with equality constraints OSNR-EC is shown to yield sublinear cumulative constraint violation. Finally, we illustrate the performance of OSNR and OSNR-EC on two numerical examples, viz., online position tracking and optimal power flow, and observe that OSNR and OSNR-EC exhibit high performance even at low sampling rates.

2026-05-26

arXiv (preprint)

PIKAN: Physics-Inspired Kolmogorov-Arnold Networks for Explainable UAV Channel Modelling

Kürşat Tekbıyık

Gunes Karabulut Kurt

Unmanned aerial vehicle (UAV) communications demand accurate yet interpretable air-to-ground (A2G) channel models that can adapt to non-stat… (see more)ionary propagation environments. While deterministic models offer interpretability and deep learning (DL) models provide accuracy, both approaches suffer from either rigidity or a lack of explainability. To bridge this gap, we propose the Physics-Inspired Kolmogorov-Arnold Network (PIKAN) that embeds physical principles (e.g., free-space path loss, two-ray reflections) into the learning process. Unlike physics-informed neural networks (PINNs), PIKAN is more flexible for applying physical information because it introduces them as adaptable inductive biases. Thus, it enables a more flexible training process. Experiments on UAV A2G measurement data show that PIKAN achieves comparable accuracy to DL models while providing symbolic and explainable expressions aligned with propagation laws. Remarkably, PIKAN achieves this performance with only 232 parameters, making it up to 37 times lighter than multilayer perceptron (MLP) baselines with thousands of parameters, without sacrificing correlation with measurements and also providing symbolic expressions. These results highlight PIKAN as an efficient, interpretable, and scalable solution for UAV channel modelling in beyond-5G and 6G networks.

2026-03-06

IEEE Aerospace Conference (published)

Practical Solutions to Volt-var Optimization under Uncertainty via Blackbox Optimization

Feng Li

Ilhan Kocar

In this work, we propose an optimal reactive power dispatch (ORPD) stochastic program for volt-var optimization (VVO) of power distribution … (see more)networks. The formulation considers not only control settings of conventional VVO devices, e.g., voltage regulators, capacitor banks, and on-load tap changers, but also optimal settings for volt-var droop curves of distributed energy resources (DERs), compliant with the IEEE 1547-2018 standard. Instead of including the power flow equations in the optimization problem which makes it nonlinear and nonconvex, a power flow solver is utilized and the problem is solved by blackbox optimization (BBO). The feasibility of the derived solution is improved by using unbalanced power flow simulations. The solution is effective under various demand and DER generation scenarios such that device settings are not frequently changed, making it practical for in-field implementations. Through numerical simulations on IEEE test feeders, we illustrate the performance of the solutions of our proposed approach on both in-sample and out-of-sample scenarios. We show that our approach outperforms a benchmark reinforcement learning method, and is also scalable to large-scale distribution networks.

2025-12-31

IEEE Transactions on Power Delivery (published)

Distributed Combined Space Partitioning and Network Flow Optimization: an Optimal Transport Approach

Théo Laurentin

Patrick Coirault

Emmanuel Moulay

Jerome Le Ny

2025-12-08

2025 IEEE 64th Conference on Decision and Control (CDC) (published)

A Comprehensive Review of Transmission and Distribution Optimal Power Flow Problems for the Integration of Distributed Energy Resources

Samuel M. Muhindo

Hanane Dagdougui

Hussein Suprême

This paper presents a comprehensive review of coordination methods for addressing large-scale transmission and distribution optimal power fl… (see more)ow (TDOPF) problems involving distributed energy resources. With distinct objectives, each transmission and distribution system operator (TSO/DSO) independently seeks to solve its own optimal power flow (OPF) instance. First, iterative methods are reviewed, in which the central OPF is solved recursively by decomposing the full problem into smaller, more manageable sub-problems or by replacing peripheral portions of the network within the central OPF with reduced equivalent grids. Generally, the convergence to an optimal solution of the full problem when all sub-OPFs are coordinated is not guaranteed as iterative methods repeat procedures until the changes in control variables of the central OPF are minimal. Second, sequential methods are reviewed, in which the central OPF is solved sequentially in a fixed, nonrepeating procedure by considering previous results. Achieving a fair balance between TSO and DSO interests in sequential methods might adversely affect the performance of a largescale central OPF. The advantages and the limitations of the two coordination methods are presented based on the operation mode of TSO-DSO network. Future research opportunities for coordination methods of TSO-DSO network are drawn using the Kron reduction method and mean-field games.

2025-10-14

2025 IEEE Electrical Power and Energy Conference (EPEC) (published)

Joint Satellite Power Consumption and Handover Optimization for LEO Constellations

Yassine Afif

Mohammed Almekhlafi

Gunes Karabulut Kurt

In satellite constellation-based communication systems, continuous user coverage requires frequent handoffs due to the dynamic topology indu… (see more)ced by the Low Earth Orbit (LEO) satellites. Each handoff between a satellite and ground users introduces additional signaling and power consumption, which can become a significant burden as the size of the constellation continues to increase. This work focuses on the optimization of the total transmission rate in a LEO-to-user system, by jointly considering the total transmitted power, user-satellite associations, and power consumption, the latter being handled through a penalty on handoff events. We consider a system where LEO satellites serve users located in remote areas with no terrestrial connectivity, and formulate the power allocation problem as a mixed-integer concave linear program (MICP) subject to power and association constraints. Our approach can be solved with off-the-shelf solvers and is benchmarked against a naive baseline where users associate to their closest visible satellite. Extensive Monte Carlo simulations demonstrate the effectiveness of the proposed method in controlling the handoff frequency while maintaining high user throughput. These performance gains highlight the effectiveness of our handover-aware optimization strategy, which ensures that user rates improve significantly, by about 40%, without incurring a disproportionate rise in the handoff frequency.

2025-10-13

International Conference on Wireless for Space and Extreme Environments (published)

On the frequency variation in load-flow calculations for islanded alternating current microgrids

Matthias Molénat

Jean Mahseredjian

Nasim Rashidirad

2025-08-31

Mathematics and Computers in Simulation (published)

Distributed Combined Space Partitioning and Network Flow Optimization: an Optimal Transport Approach (Extended Version)

Théo Laurentin

Patrick Coirault

Emmanuel Moulay

Jerome Le Ny

2025-08-28

ArXiv (preprint)