184. Analysis of Second-Order Methods via non-convex Performance Estimation
Invited abstract in session WE-2: Recent advances in computer-aided analyses of optimization algorithms I, stream Conic optimization: theory, algorithms and applications.
Wednesday, 14:10 - 15:50Room: M:O
Authors (first author is the speaker)
| 1. | Nizar Bousselmi
|
| ICTEAM, UCLouvain | |
| 2. | Anne Rubbens
|
| ICTEAM, UCLouvain | |
| 3. | Julien Hendrickx
|
| ICTEAM | |
| 4. | François Glineur
|
| ICTEAM/INMA & CORE, Université catholique de Louvain (UCLouvain) |
Abstract
The “Performance Estimation Problem framework” computes numerically the exact worst-case performance of a given optimization method on a given function class, whenever interpolation constraints for this class are available. It allowed to determine the convergence rate of numerous first-order methods and also to design optimal methods. The convex formulation of the Performance Estimation Problems can be efficiently solved but it restricted the analysis to certain types of methods. Recently, some works have been proposed to tackle a non-convex formulation of Performance Estimation Problems thanks to recent global branch and bound solvers. It allows more flexibility in the analysis but at a computational cost. In this work, we propose to exploit the non-convex Performance Estimation Problem and recently derived second-order interpolation conditions, to analyze second-order optimization methods.
Keywords
- Complexity and efficiency of optimization algorithms
Status: accepted
Back to the list of papers