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- W2182240341 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." @default.
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- W2182240341 date "2015-07-01" @default.
- W2182240341 modified "2023-10-18" @default.
- W2182240341 title "Convergence of Caratheodory solutions for primal-dual dynamics in constrained concave optimization" @default.
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- W2182240341 doi "https://doi.org/10.1137/1.9781611974072.40" @default.
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