Prediction-Correction Splittings for Nonsmooth Time-Varying Optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866909188739825664 |
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| author | Bastianello, Nicola Simonetto, Andrea Carli, Ruggero |
| author_facet | Bastianello, Nicola Simonetto, Andrea Carli, Ruggero |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_00298 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Prediction-Correction Splittings for Nonsmooth Time-Varying Optimization Bastianello, Nicola Simonetto, Andrea Carli, Ruggero Optimization and Control 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. |
| title | Prediction-Correction Splittings for Nonsmooth Time-Varying Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/1903.00298 |