Researcher at CERMICS in the Optimization team and Professor at École Nationale des Ponts et Chaussées.

Research Themes

• 2024 onwards: formal proofs, a new direction. Coq-checked proofs of conditional separation and of the Sands–Sauer–Woodrow theorem.

• 2020 onwards: information structures, games and causality with M. De Lara and B. Heymann. This includes Kuhn’s equivalence theorem (Games and Economic Behavior 2022), conditional separation and causal inference.

• 2019 onwards: tropical (min-plus) dynamic programming with M. Akian and B. Tran (CDC 2019, MTNS 2022, Annals of OR 2025).

• 2019 onwards: generalized convexity and sparsity with Michel De Lara, Seta Rakotomandimby, Adrien Le Franc, Antoine Deza and Lionel Pournin. Capra conjugacies and the ℓ₀ pseudonorm with M. De Lara, five of them in the Journal of Convex Analysis. This work extends to the geometry of norms (submitted to JMLR) and to machine learning (Fitzpatrick losses, NeurIPS 2024).

  More on Capra conjugacies and the ℓ₀ pseudonorm

  The ℓ₀ pseudonorm counts the nonzero entries of a vector and is central to exact sparse optimization. As its Fenchel biconjugate is zero, classical convex analysis fails. Instead, we develop a generalized convexity based on Capra (Constant Along Primal RAys) couplings, built from a source norm. We introduce orthant-strictly monotonic norms (e.g. ℓ_p, 1 < p < ∞) together with generalized top-k and k-support norms. With these, we prove that ℓ₀ is Capra-convex, that is, equal to its Capra-biconjugate, when the source norm and its dual are orthant-strictly monotonic. Surprisingly, ℓ₀ then coincides, on the unit sphere of the source norm, with a proper convex lower semicontinuous function ("hidden convexity"). Capra conjugates and subdifferentials yield variational formulations and new norm-ratio lower bounds for ℓ₀. We also cover a unified theory of polarity for functions, the geometry of k-support dual norms promoting k-sparse solutions, the characterization of Capra-convex sets, and a convergent Capra-cutting plane method for ℓ₀ minimization. Finally, H0-couplings extend the approach to all 0-homogeneous functions and yield their best convex lower envelopes, in particular for ℓ₀.

• 2018 onwards: multistage stochastic optimization and decomposition with Pierre Carpentier, Guy Cohen, Michel De Lara and PhD students.

  • Methods: SDDP bounds, decomposition (spatial, temporal, time blocks, two time scales) and time consistency.
  • Applications: hydro valleys, microgrids, a subway station, energy storage, hydrogen, maintenance, reservoirs, intraday markets and low-thrust space trajectories.
  More on multistage stochastic optimization and decomposition

  A first theme is the framing of such problems: information structures, non-anticipativity, risk. A second theme is decomposition–coordination: splitting large problems along time, scenarios or space. We combine these decompositions, for instance spatial coordination with dynamic programming. Time-block decomposition lets us handle two-time-scale problems with hundreds of thousands of stages. Price and resource coordination give upper and lower bounds on the optimal cost, and policies usable online. We also study time consistency, chance constraints, and the differentiability of value functions. Our energy applications include unit commitment, hydro valleys, multi-usage dams and urban microgrids. They also include battery aging and renewal, braking-energy storage in subways, and home solar with storage. We assess our methods by simulation against model predictive control.

• Ongoing: scientific software, Nsp and ScicosLab, with François Delebecque, Ramine Nikoukhah, Bruno Pinçon and others. Nsp is a GPL scientific computing environment, a complete rewrite of ScilabGtk; ScicosLab is its Scilab 4 based predecessor and the reference software of the book Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4 (Springer, 2010). See the Nsp page for details. Related work: a Premia/Nsp parallel benchmark (2010), Scicos code generation (2015) and Simulink→Modelica translation (Modelica Conference 2019).

• 2002–2013: stochastic control, finance and fixed points.

  • Impulse control and optimal stopping (with Øksendal and Sulem), and risk-sensitive portfolio optimization.
  • Single-author papers on iterative schemes for nonexpansive mappings (JMAA, Nonlinear Analysis).
  • Foundations of stochastic optimization: measurability constraints (SIAM J. Optim. 2009) and dynamic consistency.
  • Risk-averse bandit problems (Transportation Science).

• 1994–1998: PDE models in water engineering. Settling-tank models, mostly with M. (Cohen) De Lara and F. Pacard, published in SIAM J. Appl. Math., M3AS, CRAS and Water Research (3 papers). Also tracing river pollution sources and hydro scheduling by decomposition.

• 1986–1990: computer algebra for control. The Pandore expert system, with Jean-Pierre Quadrat, Agnès Sulem and Claude Gomez. It generated Fortran and LaTeX code automatically (Macrofort, Macrotex) and wrote reports on stochastic control problems.