Performance Estimation of First-Order Methods on Quadratic Functions
(2022) 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2022) — Location: Bayreuth, Germany (12.September.2022)
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- Abstract
- We are interested in determining the worst performance exhibited by a given first-order optimization method on the class of quadratic functions. Since its introduction, the Performance Estimation Problem (PEP) methodology has allowed the computation of the exact worst-case performance of first-order optimization methods on several functions classes, including smooth convex, strongly convex or nonconvex functions. In this work, we extend the PEP framework to the class of quadratic functions, and apply it to analyze the difference of performance of the gradient method between convex quadratic and general smooth convex functions.
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Citations
Bousselmi, N., Hendrickx, J., & Glineur, F. (2022). Performance Estimation of First-Order Methods on Quadratic Functions. In ed.: Baumann, Michael Heinrich ; Grüne, Lars ; Jacob, Birgit ; Worthmann, Karl (ed.), Extended Abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022 : held 12-16 September 2022 in Bayreuth, Germany (pp. 771-774). https://doi.org/10.15495/EPub_UBT_00006809