GENERALIZATION OF HYPERBOLIC SMOOTHING APPROACH FOR NON-SMOOTH AND NON-LIPSCHITZ FUNCTIONS
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, cilt.18, sa.6, ss.4511-4526, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 18 Sayı: 6
- Basım Tarihi: 2022
- Doi Numarası: 10.3934/jimo.2021170
- Dergi Adı: JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
- Sayfa Sayıları: ss.4511-4526
- Anahtar Kelimeler: Smoothing, non-Lipschitz minimization, regularization problems, MINIMIZATION
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this study, we concentrate on the hyperbolic smoothing technique for some sub-classes of non-smooth functions and introduce a generalization of hyperbolic smoothing technique for non-Lipschitz functions. We present some useful properties of this generalization of hyperbolic smoothing technique. In order to illustrate the efficiency of the proposed smoothing technique, we consider the regularization problems of image restoration. The regularization problem is recast by considering the generalization of hyperbolic smoothing technique and a new algorithm is developed. Finally, the minimization algorithm is applied to image restoration problems and the numerical results are reported.