Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Asymptotic convergence
of constrained primal-dual dynamics
A. Cherukuri, E. Mallada, J. Cortés
Systems and Control Letters 87 (2016), 10-15
Abstract
This paper studies the asymptotic convergence properties of the
primal-dual dynamics designed for solving constrained concave
optimization problems using classical notions from stability
analysis. We motivate the need for this study by providing an example
that rules out the possibility of employing the invariance principle
for hybrid automata to study asymptotic convergence. We understand the
solutions of the primal-dual dynamics in the Caratheodory sense and
characterize their existence, uniqueness, and continuity with respect
to the initial condition. We use the invariance principle for
discontinuous Caratheodory systems to establish that the primal-dual
optimizers are globally asymptotically stable under the primal-dual
dynamics and that each solution of the dynamics converges to an
optimizer.
pdf   |   ps.gz
Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo