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

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Titel: Lyapunov analyses for first-order methods: Theory, automation, and algorithm design
Autoren: Upadhyaya, Manu
Weitere Verfasser: Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Automatic Control, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för reglerteknik, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: AI and Digitalization, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: AI och digitalisering, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator, Giselsson, Pontus
Schlagwörter: Natural Sciences, Mathematical Sciences, Computational Mathematics, Naturvetenskap, Matematik, Beräkningsmatematik
Beschreibung: 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.
Dateibeschreibung: electronic
Zugangs-URL: https://lucris.lub.lu.se/ws/files/226456919/thesis.pdf
Datenbank: SwePub
Beschreibung
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.