Since Nesterov’s work in 1984, and Beck and Teboule’s FISTA algorithm (2008), it is acknowledged that using an inertial gradient algorithm instead of a classical gradient algorithm is in general much more efficient to minimize a convex functional. In particular, such an idea is the foundation of all the optimization algorithms used in deep learning where first order algorithms are the cornerstone due to the high dimension of the problems. In this talk, we shall see that the usefulness of the inertia highly depends on the geometry of the functional to minimize. As a consequence, the use of inertia is not always useful. These results have direct consequences in image processing and deep learning.
Le programme du séminaire est consultable sur la page web dédiée au Graduate Program Numeric.