@inproceedings{872308e5f95441deba51ec774c459773,
title = "Prediction-correction splittings for nonsmooth time-varying optimization",
abstract = "We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on prediction-correction, which employs splitting methods to solve the sampled instances of the time-varying problem. We describe the prediction-correction scheme and two splitting methods, the forward-backward and the Douglas-Rachford. Then by using a result for generalized equations, we prove convergence of the generated sequence of approximate optimizers to a neighborhood of the optimal solution trajectory. Simulation results for a leader following formation in robotics assess the performance of the proposed algorithm.",
keywords = "Douglas-Rachford, Forward-backward, Generalized equations, Prediction-correction, Splitting methods, Time-varying optimization",
author = "Nicola Bastianello and Andrea Simonetto and Ruggero Carli",
note = "Publisher Copyright: {\textcopyright} 2019 EUCA.; 18th European Control Conference, ECC 2019 ; Conference date: 25-06-2019 Through 28-06-2019",
year = "2019",
month = jun,
day = "1",
doi = "10.23919/ECC.2019.8795757",
language = "English",
series = "2019 18th European Control Conference, ECC 2019",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1963--1968",
booktitle = "2019 18th European Control Conference, ECC 2019",
}