Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Resource-aware discretization of accelerated
optimization flows: the heavy-ball dynamics case
M. Vaquero, P. Mestres, J. Cortés
IEEE Transactions on Automatic Control 68 (4) (2023), 2109-2124
Abstract
This paper tackles the problem of discretizing accelerated optimization flows while retaining their
convergence properties. Inspired by the success of
resource-aware control in developing efficient
closed-loop feedback implementations on digital
systems, we view the last sampled state of the
system as the resource to be aware of. The
resulting variable-stepsize discrete-time algorithms
retain by design the desired decrease of the
Lyapunov certificate of their continuous-time
counterparts. Our algorithm design employs various
concepts and techniques from resource-aware control
that, in the present context, have interesting
parallelisms with the discrete-time implementation
of optimization algorithms. These include
derivative- and performance-based triggers to
monitor the evolution of the Lyapunov function as a
way of determining the algorithm stepsize,
exploiting sampled information to enhance algorithm
performance, and employing high-order holds using
more accurate integrators of the original dynamics.
Throughout the paper, we illustrate our approach on
a newly introduced continuous-time dynamics termed
heavy-ball dynamics with displaced gradient, but the
ideas proposed here have broad applicability to
other globally asymptotically stable flows endowed
with a Lyapunov certificate.
pdf
Mechanical and Aerospace Engineering,
University of California, San Diego
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Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
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jorgilliyo