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Lyapunov analyses for first-order methods : Theory, automation, and algorithm design

Upadhyaya, Manu LU orcid (2025)
Abstract
This thesis, comprising four research papers, contributes to the field of systematic and computer-aided analyses and design of first-order methods. The first two papers focus on developing new methodologies, while the remaining two apply these techniques to refine complexity and convergence results, as well as to design new methods. A central theme of the work is the use of Lyapunov-type analyses, a structured proof technique with historical roots in the study of dynamical systems, which is widely used to establish complexity and convergence properties of first-order methods.
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author
supervisor
opponent
  • Assistant professor Stellato, Bartolomeo, Princeton University
organization
publishing date
type
Thesis
publication status
published
subject
pages
185 pages
publisher
Department of Automatic Control, Lund University
defense location
Lecture hall A, building M, Ole Römers väg 1
defense date
2025-09-26 09:15:00
ISBN
978-91-8104-589-5
978-91-8104-590-1
project
Automatic Lyapunov analysis of optimization algorithms
language
English
LU publication?
yes
id
a006046c-9dc6-446b-b625-f129587c9674
date added to LUP
2025-08-28 15:18:28
date last changed
2025-09-08 16:41:24
@phdthesis{a006046c-9dc6-446b-b625-f129587c9674,
  abstract     = {{This thesis, comprising four research papers, contributes to the field of systematic and computer-aided analyses and design of first-order methods. The first two papers focus on developing new methodologies, while the remaining two apply these techniques to refine complexity and convergence results, as well as to design new methods. A central theme of the work is the use of Lyapunov-type analyses, a structured proof technique with historical roots in the study of dynamical systems, which is widely used to establish complexity and convergence properties of first-order methods.}},
  author       = {{Upadhyaya, Manu}},
  isbn         = {{978-91-8104-589-5}},
  language     = {{eng}},
  publisher    = {{Department of Automatic Control, Lund University}},
  school       = {{Lund University}},
  title        = {{Lyapunov analyses for first-order methods : Theory, automation, and algorithm design}},
  url          = {{https://lup.lub.lu.se/search/files/226456919/thesis.pdf}},
  year         = {{2025}},
}