GENERALIZATION OF HYPERBOLIC SMOOTHING APPROACH FOR NON-SMOOTH AND NON-LIPSCHITZ FUNCTIONS
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, vol.18, no.6, pp.4511-4526, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 18 Issue: 6
- Publication Date: 2022
- Doi Number: 10.3934/jimo.2021170
- Journal Name: JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
- Journal Indexes: 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
- Page Numbers: pp.4511-4526
- Keywords: Smoothing, non-Lipschitz minimization, regularization problems, MINIMIZATION
- Süleyman Demirel University Affiliated: Yes
Abstract
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.