Title: Perspective on the analysis and design of first-order optimization algorithms
Abstract: A central goal of the optimization community is to develop algorithms with
convergence and complexity guarantees. Such guarantees both build users’ trust in
optimization methods and provide experts with tools to improve them. However, these
guarantees are often derived from intricate combinations of inequalities that offer
limited global insight, are perceived as accessible only to specialists, and may conceal
subtle and difficult-to-detect errors.
In this presentation, we present a high-level overview of systematic approaches to the
analysis and design of optimization algorithms. The discussion is illustrated through
concrete examples, highlighting how the core principles underlying these methods already
appear in classical optimization schemes.
The main methodology relies on semidefinite programming (SDP) and is implemented in the
PEPit package (https://pepit.readthedocs.io/), which
allows users to apply the framework without explicit SDP modeling or coding. This talk is
based on joint work with collaborators who will be acknowledged during the presentation.