Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes

@article{Bastianello2019PredictioncorrectionFN,
  title={Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes},
  author={Nicola Bastianello and Andrea Simonetto and Ruggero Carli},
  journal={ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  year={2019},
  pages={5581-5585}
}
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness… 

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