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

Tang, Yujie; Dall'Anese, Emiliano; Bernstein, Andrey; Low, Steven

doi:10.1137/20M1371063

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

Journal Article · Thu Jul 07 04:00:00 EDT 2022 · SIAM Journal on Control and Optimization

DOI:https://doi.org/10.1137/20M1371063· OSTI ID:1884801

Tang, Yujie; Dall'Anese, Emiliano; Bernstein, Andrey; Low, Steven

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.

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE Advanced Research Projects Agency - Energy (ARPA-E)

DOE Contract Number:: AC36-08GO28308

OSTI ID:: 1884801

Report Number(s):: NREL/JA-5D00-83850; MainId:84623; UUID:68a1f3ac-3092-40fe-a48c-3b2beb663092; MainAdminID:65237

Journal Information:: SIAM Journal on Control and Optimization, Journal Name: SIAM Journal on Control and Optimization Journal Issue: 4 Vol. 60

Country of Publication:: United States

Language:: English

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

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