After dual PhDs from Ecole Polytechnique and Stanford University in optimisation and finance, followed by a postdoc at U.C. Berkeley, Alexandre d'Aspremont joined the faculty at Princeton University as an assistant then associate professor with joint appointments at the ORFE department and the Bendheim Center for Finance. He returned to Europe in 2011 thanks to a grant from the European Research Council and is now directeur de recherche at CNRS, and professor at Ecole Normale Supérieure in Paris. He received the SIAM Optimization prize for 2004-2007, a NSF CAREER award, and an ERC starting grant. In 2016, he co-founded Kayrros, an earth observation startup. His research focuses on convex optimization and applications to machine learning, statistics, climate and finance.

Title:

Shapley-Folkman, Frank-Wolfe and Nonconvex Separable Problems

Abstract:

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the average becomes much larger than the ambient dimension. In optimization, this produces a priori bounds on the duality gap of nonconvex separable problems involving finite sums. We show how to systematically recover solutions of convex relaxations using Frank Wolfe, while ensuring that these solutions satisfy the above duality gap bounds. Finally, we detail applications of these results to feature selection problems such as sparse Naive Bayes, LASSO, etc.

After finishing her undergraduate math studies in Argentina, Claudia moved to Paris where she obtained her PhD and habilitation degrees. Personal reasons caused Claudia to reverse direction over the Atlantic Ocean; she now lives in Rio de Janeiro.

Claudia has participated in industrial collaborations since the time of her PhD studies. Her first experience in this area, with Electricité de France, was so beneficial that it greatly influenced her career: Claudia’s theoretical research has been continuously enriched with insight provided by real life problems. 

She is an applied mathematician specialized in optimization, both its theory and its numerical aspects. Her research interests lie primarily in the area of nonsmooth optimization, stochastic programming, and variational analysis, with an emphasis on applications in the energy sector.

Title:

Working out the accuracy/speed dilemma in nonsmooth optimization 

Abstract:

For many years, the development of superlinearly convergent algorithms for nonsmooth problems was considered science fiction, an impossible task. The paradigm shifted after it was realized that many functions are not differentiable according to certain special construction called manifold of smoothness. It was then possible to algorithmically track these manifolds using inexact variants of the proximal point algorithm, implemented as in a bundle method. The goal of achieving greater accuracy then became a reality, but at the cost of reduced performance in terms of overall execution time, as the associated calculations involved significant additional work. To increase accuracy, the curvature of the smooth manifold must be identified by examining the structural properties of the function to be minimized. We consider additive structures and discuss cases where it is possible to improve the accuracy of the proximal gradient method without compromising its well-known speed of execution. 

Kim-Chuan Toh is the Leo Tan Professor in the Department of Mathematics at the National University of Singapore.

He works extensively on convex programming, particularly large-scale matrix optimization problems such as semidefinite programming,

and optimization problems arising from machine learning and statistics.

Currently he serves as a co-Editor for Mathematical Programming, an Area Editor for Mathematical Programming Computation,

an Associate Editor for SIAM J. on Optimization, Operations Research, and ACM Transactions on Mathematical Software.

He received the INFORMS Optimization Society Farkas Prize in 2017 and the triennial Mathematical Optimization Society Beale-Orchard Hays Prize in 2018.

He is a Fellow of SIAM.

Title: 

Recent advances on algorithms for solving doubly nonnegative relaxations of mixed-binary quadratic programs 

Abstract:

As a powerful relaxation of the completely positive conic reformulation of a mixed-binary quadratic program (MBQP), doubly nonnegative (DNN) relaxation can usually provide a tight lower bound. However, DNN programming problems are known to be challenging to solve because of their huge number of $\Omega(n^2)$ constraints and $\Omega(n^2)$ variables. In this talk, we present some recent advances on algorithms for solving DNN problems and related variants. In particular, we introduce the algorithm RiNNAL, a method for solving DNN relaxations of large-scale MBQPs by leveraging their solutions’ possible low-rank property. RiNNAL is a globally convergent Riemannian based augmented Lagrangian method (ALM) that penalizes the nonnegative and complementarity constraints while preserving all other constraints

as an algebraic variety in the ALM subproblem. After applying low-rank factorization in the subproblem, its feasible region becomes an algebraic variety with favorable geometric properties. We make the crucial step to equivalently reformulate most of the quadratic constraints in the factorized model into fewer and more manageable affine constraints. Moreover, we show that the retraction operation, which is the 

metric projection onto the variety, although non-convex, can be computed efficiently through an equivalent

convex reformulation under certain regularity conditions. Numerous numerical experiments will be presented to validate the efficiency of the proposed algorithm. [This talk is based mainly on joint work with Di Hou and Tianyun Tang]

Stephen J. Wright is the George B. Dantzig Professor of Computer Sciences, Sheldon Lubar Chair of Computer Sciences, and Hilldale Professor at the University of Wisconsin-Madison. He also serves as Chair of the Computer Sciences Department. His research is in computational optimization and its applications to data science and many other areas of science and engineering.

Prior to joining UW-Madison in 2001, Wright held positions at North Carolina State University (1986-1990) and Argonne National Laboratory (1990-2001). He has served as Chair of the Mathematical Optimization Society (MOS) from 2007-2010 and was elected to the Board of Trustees of SIAM for the maximum three terms, from 2005-2014.

He was elected to the National Academy of Engineering in 2024. In the same year, he received the George B. Dantzig Prize, awarded jointly by MOS and SIAM, for "original research having a major impact on mathematical optimization." In 2020, he was awarded the Khachiyan Prize by the INFORMS Optimization Society for "lifetime achievements in the area of optimization," and also received the NeurIPS Test of Time Award. He became a Fellow of SIAM in 2011. In 2014, he won the W.R.G. Baker Award from IEEE for best paper in an IEEE archival publication during 2009-2011.

Prof. Wright is the author/coauthor of widely used text and reference books in optimization including "Primal Dual Interior-Point Methods" and "Numerical Optimization." He has published widely on optimization theory, algorithms, software, and applications.

Prof. Wright served from 2014-2019 as Editor-in-Chief of the SIAM Journal on Optimization and previously served as Editor-in-Chief of Mathematical Programming Series B. He has also served as Associate Editor of Mathematical Programming Series A, SIAM Review, SIAM Journal on Scientific Computing, and several other journals and book series.

Title: 

Gradient-Based Methods for Large-Scale Bilevel Optimization 

Abstract:

Bilevel optimization has emerged as a powerful framework across such machine learning applications as reinforcement learning and language model fine-tuning, as well as in game-theoretic modeling. As these problems scale, so too does the need for principled, efficient algorithms that can handle stochasticity and structural complexity. This talk will discuss recent advances in scalable, gradient-based

methods for bilevel problems with smooth objectives, where gradients are accessed only through unbiased stochastic oracles. First, we consider the foundational case in which the lower-level problem is strongly convex, and establish non-asymptotic convergence guarantees for finding an epsilon-approximate stationary point.  Second, we explore two active frontiers: (1) extensions to fully nonconvex objectives, including settings with lower-level constraints, and (2) new complexity lower bounds informed by different oracle models. Together, these results form a unified theoretical framework for understanding and designing gradient-based bilevel solvers at scale. Finally, we sketch emerging challenges and opportunities in bilevel optimization, particularly at the intersection of optimization theory and modern machine learning practice.

(Joint work with Jeongyeol Kwon, Dohyun Kwon, Rob Nowak)