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
-
Multi-agent online optimization with delays: Asynchronicity, adaptivity, and optimism
YG. Hsieh, F. Iutzeler, J. Malick, P. Mertikopoulos
-
The last-iterate convergence rate of optimistic mirror descent in stochastic variational inequalities
Waiss Azizian, Franck Iutzeler, Jerome Malick, Panayotis Mertikopoulos
-
Proximal gradient methods with adaptive subspace sampling
Dmitry Grishchenko, Franck Iutzeler, Jerome Malick
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
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
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
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 ?