Publications
Click here for an overview of my PhD objectives achived so far.
Managing uncertainties in multistage stochastic optimization poses a substantial challenge, necessitating a a complex trade-off between, on the one hand, the representation of the uncertainties (i.e. the number of scenarios) and, on the other hand, the computational tractability. Scenario reduction methods, pioneered in 2003 by Dupavcova et al., offer a promising outlooks for achieving a satisfactory trade-off. However, the choice of distance metric for reducing scenario trees significantly influences solution quality. While clustering techniques have been prevalent, recent research has turned to Wasserstein-based methods to minimize transport distance between probabilty measures.
My work presents a comprehensive investigation of the use of Wasserstein distance for scenario tree reduction in the context of multistage stochastic optimization. The Wasserstein barycenter (WB) serves as a tool for summarizing sets of probabilities, it appears in a number of disciplines, including applied probability, clustering and image processing. Numerically efficient methods to computing the WB rely on entropic regularization functions, resulting in approximate solutions due to limitations in solver capabilities. In contrast, this research introduces an exact approach based on the Douglas-Rachford splitting method directly applied to the WB linear optimization problem. The proposed solving algorithm achieves a trade-off between the numerical efficiency of regularization-based methods and the precision of exact LP solvers.
Kovacevic and Pichler develop a reduction algorithm based on nested Wasserstein distance. This algorithm consists of computing a significant amount of Wasserstein barycenters. The second contribution of this work is to implement dedicated WB computation algorithms, including the Iterative Bregmann Projection method (IBP), Sinkhorn distance, and the newly introduced Method of Averaged Marginals (MAM) in the algorithm proposed in their work, Kovacevic and Pichler, to accelerate its performances.
By proposing efficient algorithms for computing Wasserstein barycenters and reducing scenario trees, we address critical challenges in managing uncertainties in multistage stochastic optimization. Looking ahead, future research directions include further exploration of the interplay between optimization algorithms and stochastic processes to refine scenario tree reduction methodologies and enhance the applicability of Wasserstein-based methods in complex optimization problems.
Journal papers
| J1 | Mimouni, D., Malisani, P., Zhu, J., & de Oliveira, W. (2023). Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals. arXiv preprint arXiv:2309.05315. |
| To appear in SIAM Journal on Mathematics of Data Science (SIMODS) | |
| Link: website / paper PDF / codes . |
Conference contributions
| NC1 | Mimouni, D.(2023). Advances in Variational Analysis and Nonsmooth Optimization: Computing Wasserstein Barycenter via Operator Splitting: the Method of Averaged Marginals, July 2024. |
| Presentation during the 25th International Symposium on Mathematical Programming | |
| Link: slides (not up to date). | |
| NC2 | Mimouni, D.(2023). A new approach for computing Wasserstein Barycenter via operator splitting in the classical balanced setting, Nov 2023. |
| Presentation during the PGMO days | |
| Link: slides / Presentation (video) on demand. | |
| NC3 | Mimouni, D.(2023). About the Wasserstein Barycenter, April 2023. |
| Presentation during the CIROQUO conference | |
| Links: Poster . |
PhD Mid-term Report
| R1 | Mimouni, D.(2023). Scenario Tree Reduction and Operator Splitting Method for Stochastic Optimization of Energy Systems |
| This report corresponds to the researchs I have carried on up to April 2024. I also presented my research at the industrial annual meeting for PhD student in IFP énergie nouvelles. | |
| Links: Report / Slides . |