Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimization

Andrey Bernstein, Emiliano Dall'Anese, Andrea Simonetto

Research output: Contribution to journalArticlepeer-review

63 Scopus Citations


This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging time-varying convex optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level operational constraints. Departing from existing batch and feed-forward optimization approaches, the design of the algorithms capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate feedback from the system in the form of measurements, hence, the term 'online optimization with feedback.' By virtue of this approach, the resultant algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, analytical convergence claims are established in terms of dynamic regret. Furthermore, when the synthesis of the feedback-based online algorithms is based on a regularized Lagrangian function, \boldsymbol{Q}-linear convergence to solutions of the time-varying optimization problem is shown.

Original languageAmerican English
Article number8631190
Pages (from-to)1978-1991
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - 15 Apr 2019

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-71874


  • convex optimization
  • feedback
  • Online optimization
  • primal-dual methods


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