Prediction-Correction Algorithms for Time-Varying Constrained Optimization

Emiliano Dall-Anese, Andrea Simonetto

Research output: Contribution to journalArticlepeer-review

56 Scopus Citations

Abstract

This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do not require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.
Original languageAmerican English
Pages (from-to)5481-5494
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume65
Issue number20
DOIs
StatePublished - 2017

NREL Publication Number

  • NREL/JA-5D00-67655

Keywords

  • non-stationary optimization
  • parametric programming
  • prediction-correction methods
  • real-time control of energy resources
  • time-varying optimization

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