Research

Preprints

Mean field optimization problems: stability results and Lagrangian discretization.

K. Liu and L. Pfeiffer, 2023.

A mesh-independent method for second-order potential mean field games.

K. Liu and L. Pfeiffer, 2023.

Journal articles

Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution.

J.F. Bonnans, K. Liu, N. Oudjane, L. Pfeiffer, and C. Wan. SIAM Journal on Optimization, 2023.

[Journal] [ArXiv]

Error estimates of a theta-scheme for second-order mean field games.

J.F. Bonnans, K. Liu, and L. Pfeiffer. ESAIM: Mathematical Modeling and Numerical Analysis, 2023.

[Journal] [ArXiv]

Approximate Nash equilibria in large nonconvex aggregative games.

K. Liu, N. Oudjane, and C. Wan. Mathematics of Operations Research, 2022.

[Journal] [ArXiv]

Conference proceedings

Decomposed resolution of finite-state aggregative optimal control problems.

K. Liu, N. Oudjane, and L. Pfeiffer. SIAM CT23, 2023.

[Proceeding]

Presentations

2024.03, SPOC seminar, Non-convex aggregative and mean-field optimization problems, Institut de Mathématiques de Bourgogne, France.
2024.02, DCN-AvH seminar, Aggregative optimization problems and their mean-field relaxation, FAU Erlangen-Nürnberg, German.
2023.10, Ph.D. Defense, Numerical analysis and methods for mean-field type optimization problems, video link, Ecole Polytechnique, France.
2023.07, SIAM CT23, Decomposed resolution of finite-state aggregative optimal control problems, Philadelphia, U.S.A.
2023.06, FiME PhD seminar, Error estimates of a theta-scheme of second-order mean field games (blackboard), Institut Henri-Poincaré, France.
2023.05, Congrès SMAI 2023, Error estimates of a theta-scheme of second-order mean field games, Le Gosier, Guadeloupe.
2023.02, Paris Saclay PhD's seminar, Mean field games and a theta-scheme, Orsay, France.
2022.11, PGMO Days, Error estimates of a Theta-scheme of second-order mean field games, EDF-Lab Saclay, France.
2022.10, Hankou Road seminar, Mean field games: an introduction to the theory and numerical methods, by Zoom, Nanjing University, China.
2022.10, FiME seminar, Large-scale nonconvex optimization, Institut Henri-Poincaré, France.
2022.09, KouShare, Mean field games: an introduction, by Zoom, Bilibili link, China.
2022.06, SMAI-MODE, Large scale nonconvex optimization (poster), Limoges University, France.
2022.05, FGP22, Nonconvex optimization and randomization, Faculty of Economics of the University of Porto, Portugal.
2021.12, PGMO Days, Large nonconvex aggregative games, EDF-Lab Saclay, France.

Thesis

K. Liu, Numerical analysis and methods for mean-field type optimization problems. Ph.D. Thesis at École Polytechnique, 2023. [HAL]
K. Liu, Data-driven Methods for Uncertainty Quantification Analysis. Master 1 Thesis at TotalEnergies, 2019.