Publications

5 selected recent publications

(one/year over the last 5 years)
  • Universal generalization guarantees for WDRO [preprint]
    Tam Le, Jerome Malick

  • Harnessing structure in composite nonsmooth minimization
    Gilles Bareilles, Franck Iutzeler, Jerome Malick
    SIAM Journal on Optimization (2023) [paper] [preprint]

  • Multi-agent online optimization with delays: Asynchronicity, adaptivity, and optimism
    YG. Hsieh, F. Iutzeler, J. Malick, P. Mertikopoulos
    Journal of Machine Learning Research (2022) [paper][preprint]

  • The last-iterate convergence rate of optimistic mirror descent in stochastic variational inequalities
    Waiss Azizian, Franck Iutzeler, Jerome Malick, Panayotis Mertikopoulos
    Conference on Learning Theory (COLT) (2021) [paper][preprint]

  • Proximal gradient methods with adaptive subspace sampling
    Dmitry Grishchenko, Franck Iutzeler, Jerome Malick
    Mathematics of Operations Research (2020) [paper][preprint]

My personal top-5

  • Local linear convergence for alternating nonconvex projections
    Adrian Lewis, Russel Luke, Jerome Malick
    Foundations of Computational Mathematics (2009) [paper][preprint]
    The first study in the non-convex setting of the simple and fundamental algorithm of alternating projections. This gives nice illustrations on how geometry controls convergence: see e.g. the idea of the proof of Theorem 5.2 (page 14 in the preprint).

  • Cut-generating functions and S-free sets
    M. Conforti, G. Cornuejols, A. Daniilidis, C. Lemarechal, J. Malick
    Mathematics of Operations Research (2014) [paper][preprint]
    This paper establishes the basis of a theory of cut-generating functions, a fundamental tool in combinatorial optimization. Nice fact: this theory is grounded on convex geometry -- and even subtle new results (we needed the smallest representation of pre-polars of convex sets; see Theorem 3.8). The proof of Theorem 5.1 required creativity and abnegation; we got both from geometrical constructions.

  • U-Newton methods for nonsmooth convex minimization
    Scott Miller, Jerome Malick
    Mathematical Programming (2005) [paper][preprint]
    Newton is everywhere ! This paper reveals the connection between (i) U-Newton methods from nonsmooth optimization, (ii) Riemannian Newton methods, and (iii) standard Newton methods (SQP) of non-linear optimization The paper is not easy to read; you may prefer this one, which is a follow-up treating the non-convex case.

  • Decomposition algorithm for large-scale two-stage unit-commitment
    Wim van Ackooij, Jerome Malick
    Annals of Operations Research (2016) [paper][preprint]
    How to save carbon emission (and money)? Include stochasticity in the electricity park management model. We propose an effective algorithm to solve resulting large-scale optimization problem.

  • Harnessing structure in composite nonsmooth minimization
    Gilles Bareilles, Franck Iutzeler, Jerome Malick
    To appear in SIAM Journal on Optimization [preprint]
    My lastest paper already in my top five ? I might have given too much heart in this one... Anyway, if you think you know all about the proximal mapping, check out Theorem 3.2 (page 9) and you'll be surprised! The prox implicity identifies relevant sub-manifolds, for a specific range of prox-parameters, as illustrated on this picture for max-functions. Property both surprising and useful to design superlinear algorithms minimizing nonsmooth functions, as the max-eigenvalue of a parametrized matrice.

Last highlight: "apply mechanics to maths" as JJ Moreau said... or vice-versa ?

  • A formulation of the linear discrete Coulomb friction problem via convex optimization
    Vincent Acary, Florent Cadoux, Claude Lemarechal, Jerome Malick
    ZAMM (Journal of Applied Maths and Mechanics) [paper][preprint]
    I worked on applications of optim' in computer vision, electricity, learning obviously - but also in mechanics, with my former colleagues of the bipop/tripop team, where I belong back in my inria days :) In this paper, we isolate the convexity in the problems with contact/friction.