Exponential convergence of distributed primal–dual convex optimization algorithm without strong convexity

This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map...

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Vydané v:	Automatica (Oxford) Ročník 105; s. 298 - 306
Hlavní autori:	Liang, Shu, Wang, Le Yi, Yin, George
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.07.2019
Predmet:	Convex optimization without strong convexity Distributed optimization Exponential convergence Metric subregularity Primal–dual algorithm Rate of convergence Variational analysis Exponential convergence Metric subregularity Variational analysis Distributed optimization Convex optimization without strong convexity Rate of convergence Primal–dual algorithm
ISSN:	0005-1098, 1873-2836
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Popis
Shrnutí:	This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler’s approximation method.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/j.automatica.2019.04.004