We consider minimizing a twice-differentiable, L-smooth, and\(\mu\)-strongly convex
objective\(\phi\) over an\(n\times n\) positive semidefinite matrix\(M\succeq 0\), under the …

We study the optimization landscape of deep linear neural networks with square loss. It is
known that, under weak assumptions, there are no spurious local minima and no local …

Optimal control problems can be solved via a one-shot (single) optimization or a sequence
of optimization using dynamic programming (DP). However, the computation of their global …

We study the identification of a linear time-invariant dynamical system affected by large-and-
sparse disturbances modeling adversarial attacks or faults. Under the assumption that the …

The restricted isometry property (RIP) is a well-known condition that guarantees the absence
of spurious local minima in low-rank matrix recovery problems with linear measurements. In …

We study the identification of a linear time-invariant dynamical system affected by large-and-
sparse disturbances modeling adversarial attacks or faults. Under the assumption that the …

The reliability of the electric power grid is increasingly linked to the reliability of measured
data which is used to understand the current state of the system. Determining the current …

The paper is concerned with the theoretical explanation of the recent empirical success of
solving the low-rank matrix sensing problem via nonconvex optimization. It is known that …

Dans cette thèse, nous étudions différents aspects théoriques de l'apprentissage profond,
en particulier l'optimisation, la robustesse et l'approximation. Optimisation: Nous étudions le …

Dynamic programming (DP) has a rich theoretical foundation and a broad range of
applications, especially in the classic area of optimal control and the recent area of …