Focus Period lund 2026
Postdoctoral Researcher
French Institute for Research in Computer Science and Automation – Inria (France)
Manu Upadhyaya is a postdoctoral researcher at Inria Paris, working with Adrien Taylor, and his research interests center on continuous optimization and its applications. He earned his PhD from Lund University in 2025, where he worked on systematic and computer-aided analysis and design of first-order methods for structured optimization and inclusion problems under the supervision of Pontus Giselsson and Sebastian Banert. Prior to his doctoral studies, he completed an MSc in Engineering Physics (2020), an MSc in Finance (2020), and a BSc in Mathematics (2015), all from Lund University.
Presenting: The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods
We introduce AutoLyap, a software suite that assists with Lyapunov analyses of a wide class of first-order methods for structured optimization and inclusion problems. Lyapunov analyses are structuredproof patterns, with historical roots in the study of dynamical systems, commonly used to establish convergence results for first-order methods. Building on previous work, the core idea behind AutoLyap is to recast the verification of the existence of a Lyapunov analysis as a semidefinite program (SDP), which can then be solved numerically using standard SDP solvers. Users of the package specify (i) the classof optimization or inclusion problems, (ii) the first-order method in question, and (iii) the type of Lyapunov analysis they wish to test. Once these inputs are provided, AutoLyap handles the SDP modeling and proceeds to solve the SDP numerically. We use the package to numerically verify and extend several convergence results. AutoLyap is currently available in Python and Julia.