Scalable Distributed Algorithms for Finding Least Squares Solutions to Linear Algebraic Equations via Scheduling
Presenter: Dr. Shenyu Liu
DEIB - Alpha Room (Bld. 24)
December 9th, 2024 | 11.30 am
Contacts: Proff. Gian Paolo Incremona, Patrizio Colaneri
DEIB - Alpha Room (Bld. 24)
December 9th, 2024 | 11.30 am
Contacts: Proff. Gian Paolo Incremona, Patrizio Colaneri
Abstract
On December 9th, 2024 at 11.30 am the seminar titled "Scalable Distributed Algorithms for Finding Least Squares Solutions to Linear Algebraic Equations via Scheduling" will take place at DEIB Alpha Room (Building 24).
The least squares (LS) solutions to linear algebraic equations (LAEs) are fundamental to numerous scientific and engineering disciplines, including data fitting, principal component analysis, Kalman filters, and network analysis. Distributed algorithms for finding LS solutions to LAEs have been extensively studied to address the growing scale and complexity of these problems. However, traditional centralized and many existing distributed methods face significant challenges from computational and communication constraints. This talk introduces novel advancements in scalable distributed algorithms designed to overcome these limitations. In this talk, we introduce two discrete-time distributed LS algorithms tailored for networks with limited memory, computational power, and bandwidth. The first algorithm utilizes a nested-loop structure with alternating consensus and projection, achieving practical convergence under spanning and periodic scheduling sequences. The second algorithm enhances performance by introducing internal integrator variables, ensuring exponential convergence while requiring each agent to transmit only a fraction of its guessed solution at each iteration. Moreover, with slight modifications, this algorithm demonstrates robust solution-tracking performance for LAEs with time-varying observation vectors. Both algorithms are supported by rigorous theoretical analysis and validated through numerical simulations. By addressing the scalability and efficiency of distributed LS solutions to LAEs, this talk highlights the potential of these algorithms to handle large-scale systems while preserving privacy and adapting to real-world communication constraints.
Shenyu Liu received his B. Eng. degree in Mechanical Engineering and B.S. degree in Mathematics from the National University of Singapore, Singapore, in 2014. He received his M.S. degree in Mechanical Engineering from the University of Illinois at Urbana-Champaign, in 2015, where he also received his Ph.D. degree in Electrical and Computer Engineering in 2020. He then spent two years in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego, as a postdoctoral researcher. Since 2022, he is an assistant professor in the School of Automation at Beijing Institute of Technology, Beijing, China. His current research interest includes stability theory of switched/hybrid systems, Lyapunov methods for nonlinear systems, matrix perturbation theory, distributed algorithms, and data-driven controller design.
The least squares (LS) solutions to linear algebraic equations (LAEs) are fundamental to numerous scientific and engineering disciplines, including data fitting, principal component analysis, Kalman filters, and network analysis. Distributed algorithms for finding LS solutions to LAEs have been extensively studied to address the growing scale and complexity of these problems. However, traditional centralized and many existing distributed methods face significant challenges from computational and communication constraints. This talk introduces novel advancements in scalable distributed algorithms designed to overcome these limitations. In this talk, we introduce two discrete-time distributed LS algorithms tailored for networks with limited memory, computational power, and bandwidth. The first algorithm utilizes a nested-loop structure with alternating consensus and projection, achieving practical convergence under spanning and periodic scheduling sequences. The second algorithm enhances performance by introducing internal integrator variables, ensuring exponential convergence while requiring each agent to transmit only a fraction of its guessed solution at each iteration. Moreover, with slight modifications, this algorithm demonstrates robust solution-tracking performance for LAEs with time-varying observation vectors. Both algorithms are supported by rigorous theoretical analysis and validated through numerical simulations. By addressing the scalability and efficiency of distributed LS solutions to LAEs, this talk highlights the potential of these algorithms to handle large-scale systems while preserving privacy and adapting to real-world communication constraints.
Shenyu Liu received his B. Eng. degree in Mechanical Engineering and B.S. degree in Mathematics from the National University of Singapore, Singapore, in 2014. He received his M.S. degree in Mechanical Engineering from the University of Illinois at Urbana-Champaign, in 2015, where he also received his Ph.D. degree in Electrical and Computer Engineering in 2020. He then spent two years in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego, as a postdoctoral researcher. Since 2022, he is an assistant professor in the School of Automation at Beijing Institute of Technology, Beijing, China. His current research interest includes stability theory of switched/hybrid systems, Lyapunov methods for nonlinear systems, matrix perturbation theory, distributed algorithms, and data-driven controller design.
