Public Thesis Defense of Nizar BOUSSELMI - ICTEAM
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Performance analysis of primal-dual and second-order optimization methods by Nizar BOUSSELMI -
Tuesday, 02 September 2025 at 4:00 p.m. - Room SUD09 - Place Croix du Sud - 1348 Louvain-la-Neuve
Optimization theory develops methods to solve optimization problems. One common way to assess the quality of an optimization method is through its worst-case guarantee over a problem class. The Performance Estimation Problem (PEP) methodology makes it possible to determine the exact worst-case performance of an optimization method in a computer-assisted way.
We generalize the PEP methodology to first-order methods involving linear operators. This extension requires an explicit formulation of interpolation conditions for those linear operators. We also extend the framework to analyze the performance of first-order methods on quadratic functions. We then investigate primal-dual methods such as the Chambolle-Pock and Condat-Vu methods and improve and extend the existing analysis of their convergence.
Then, we develop interpolation conditions for classes of univariate Hessian Lipschitz and univariate generalized self-concordant functions. We exploit these conditions together with the PEP framework to analyze the convergence of second-order optimization methods such as Newton's method and its regularized variants.
This allows to obtain new tight analytical and numerical guarantees on these methods for univariate functions.
Jury members
- Prof. François Glineur (UCLouvain) (Supervisor)
- Prof. Julien Hendrickx (UCLouvain) (Supervisor)
- Prof. Pierre-Antoine Absil (UCLouvain) (Chairperson)
- Prof. Geovani Nunes Grapiglia (UCLouvain) (Secretary)
- Prof. Etienne de Klerk (University of Tilburg, Netherlands)
- Dr. Laurent Condat (KAUT, Saudi Arabia)
- Dr. Adrien Taylor (Inria, France)