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Published August 2022 | Published + Submitted
Journal Article Open

Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

Abstract

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush--Kuhn--Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.

Additional Information

© 2022 Society for Industrial and Applied Mathematics. Submitted: 19 October 2020. Accepted: 01 March 2022. Published Online: 07 July 2022. This work was supported by the ARPA-E through grant DE-AR0000699, and by the NSF through grants CCF 1637598, ECCS 1619352, CPS 1739355.

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Published - 20m1371063.pdf

Submitted - 1812.00613.pdf

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Additional details

Created:
August 22, 2023
Modified:
October 23, 2023