Prediction-Correction Algorithms for Time-Varying Constrained Optimization

doi:10.1109/TSP.2017.2728498

Title: Prediction-Correction Algorithms for Time-Varying Constrained Optimization

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This article 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.

Authors:

Simonetto, Andrea ^[1] ; Dall'Anese, Emiliano ^[2]

IBM Research, Dublin (Ireland)
National Renewable Energy Lab. (NREL), Golden, CO (United States)

Publication Date:: 2017-07-26

Report Number(s):: NREL/JA-5D00-67655
Journal ID: ISSN 1053-587X

Grant/Contract Number:: AC36-08GO28308

Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Signal Processing

Additional Journal Information:: Journal Volume: 65; Journal Issue: 20; Journal ID: ISSN 1053-587X

Publisher:: IEEE

Research Org:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org:: USDOE Office of Energy Efficiency and Renewable Energy (EERE); NREL Laboratory Directed Research and Development (LDRD)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; time-varying optimization; non-stationary optimization; parametric programming; prediction-correction methods; real-time control of energy resources

OSTI Identifier:: 1394904


                    Simonetto, Andrea, and Dall'Anese, Emiliano. Prediction-Correction Algorithms for Time-Varying Constrained Optimization.  United States: N. p.,  
        Web.  doi:10.1109/TSP.2017.2728498.

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                    Simonetto, Andrea, & Dall'Anese, Emiliano. Prediction-Correction Algorithms for Time-Varying Constrained Optimization.  United States.  doi:10.1109/TSP.2017.2728498.

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                    Simonetto, Andrea, and Dall'Anese, Emiliano. 2017.  
        "Prediction-Correction Algorithms for Time-Varying Constrained Optimization".  United States.  
        doi:10.1109/TSP.2017.2728498.  https://www.osti.gov/servlets/purl/1394904.

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@article{osti_1394904,

  title        = {Prediction-Correction Algorithms for Time-Varying Constrained Optimization},

  author       = {Simonetto, Andrea and Dall'Anese, Emiliano},

  abstractNote = {This article 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.},

  doi          = {10.1109/TSP.2017.2728498},

  journal      = {IEEE Transactions on Signal Processing},

  number       = 20,

  volume       = 65,

  place        = {United States},

  year         = {2017},

  month        = {7}

}

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10.1109/TSP.2017.2728498
https://doi.org/10.1109/TSP.2017.2728498

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