A Proximal Variable Smoothing for Nonsmooth Minimization Involving Weakly Convex Composite with MIMO Application
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908338830180352 |
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| author | Kume, Keita Yamada, Isao |
| author_facet | Kume, Keita Yamada, Isao |
| contents | We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting algorithm with two steps: (i) a time-varying forward step with the gradient of a smoothed surrogate function, designed with the Moreau envelope, of the sum of two functions; (ii) the backward step with a proximity operator of the remaining function. For the proposed algorithm, we present a convergence analysis in terms of a stationary point by using a newly smoothed surrogate stationarity measure. As an application of the target problem, we also present a formulation of multiple-input-multiple-output (MIMO) signal detection with phase-shift keying. Numerical experiments demonstrate the efficacy of the proposed formulation and algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proximal Variable Smoothing for Nonsmooth Minimization Involving Weakly Convex Composite with MIMO Application Kume, Keita Yamada, Isao Optimization and Control We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting algorithm with two steps: (i) a time-varying forward step with the gradient of a smoothed surrogate function, designed with the Moreau envelope, of the sum of two functions; (ii) the backward step with a proximity operator of the remaining function. For the proposed algorithm, we present a convergence analysis in terms of a stationary point by using a newly smoothed surrogate stationarity measure. As an application of the target problem, we also present a formulation of multiple-input-multiple-output (MIMO) signal detection with phase-shift keying. Numerical experiments demonstrate the efficacy of the proposed formulation and algorithm. |
| title | A Proximal Variable Smoothing for Nonsmooth Minimization Involving Weakly Convex Composite with MIMO Application |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.10934 |