A Proximal Variable Smoothing for Minimization of Nonlinearly Composite Nonsmooth Function -- Maxmin Dispersion and MIMO Applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908396282707968 |
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| author | Kume, Keita Yamada, Isao |
| author_facet | Kume, Keita Yamada, Isao |
| contents | We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure inspired by a proximal gradient-type method. More precisely, the proposed algorithm consists of two steps: (i) a gradient descent of a time-varying smoothed surrogate function designed partially with the Moreau envelope of the weakly convex function; (ii) an application of the proximity operator of the remaining function not covered by the smoothed surrogate function. We also present a convergence analysis of the proposed algorithm by exploiting a novel asymptotic approximation of a gradient mapping-type stationarity measure. Numerical experiments demonstrate the effectiveness of the proposed algorithm in two scenarios: (i) maxmin dispersion problem and (ii) multiple-input-multiple-output (MIMO) signal detection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Proximal Variable Smoothing for Minimization of Nonlinearly Composite Nonsmooth Function -- Maxmin Dispersion and MIMO Applications Kume, Keita Yamada, Isao Optimization and Control Signal Processing We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure inspired by a proximal gradient-type method. More precisely, the proposed algorithm consists of two steps: (i) a gradient descent of a time-varying smoothed surrogate function designed partially with the Moreau envelope of the weakly convex function; (ii) an application of the proximity operator of the remaining function not covered by the smoothed surrogate function. We also present a convergence analysis of the proposed algorithm by exploiting a novel asymptotic approximation of a gradient mapping-type stationarity measure. Numerical experiments demonstrate the effectiveness of the proposed algorithm in two scenarios: (i) maxmin dispersion problem and (ii) multiple-input-multiple-output (MIMO) signal detection. |
| title | A Proximal Variable Smoothing for Minimization of Nonlinearly Composite Nonsmooth Function -- Maxmin Dispersion and MIMO Applications |
| topic | Optimization and Control Signal Processing |
| url | https://arxiv.org/abs/2506.05974 |