Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Convergence of Caratheodory solutions for primal-dual
dynamics in constrained concave optimization
A. Cherukuri, E. Mallada, J. Cortés
Proceedings of the SIAM Conference on Control and Its Applications,
Paris, France, 2015, pp. 290-296
Abstract
This paper characterizes the asymptotic convergence properties of
the primal-dual dynamics to the solutions of a constrained concave
optimization problem using classical notions from stability
analysis. We motivate our study by providing an example which rules
out the possibility of employing the invariance principle for hybrid
automata to analyze the asymptotic convergence. We understand the
solutions of the primal-dual dynamics in the Caratheodory sense and
establish their existence, uniqueness, and continuity with respect to
the initial conditions. We employ the invariance principle for
Caratheodory solutions of a discontinuous dynamical system to show
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.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
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cortes at ucsd.edu
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