Open AccessGeneralization of hyperbolic smoothing approach for non-smooth and non-Lipschitz functions
Author(s) -
Nurullah Yılmaz,
Ahmet Şahiner
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021170
Subject(s) - smoothing , lipschitz continuity , generalization , regularization (linguistics) , inverse hyperbolic function , mathematics , hyperbolic function , mathematical optimization , algorithm , computer science , mathematical analysis , artificial intelligence , hyperbolic manifold , statistics
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.