<p style='text-indent:20px;'>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.</p>

In this study, we introduce a new smoothing approximation to the non-differentiable exact penalty functions for inequality constrained optimization problems. Error estimations are investigated between non-smooth penalty function and smoothed penalty function. In order to demonstrate the effectiveness of proposed smoothing approach the numerical examples are given.

Macrosiphum rosae (L.) is one of the most destructive pests for Rosa damascena (Miller) when it is found in high numbers. In order to understand the population dynamics of this pest, our priority should be the determination of what extent environmental factors affect the pest population. In this study, we apply fuzzy logic modeling to visualize the population variations, which depends on the environmental factors (temperature and humidity), by using the data obtained from the field studies. After that, we determine the values of temperature and humidity that makes the number of M. rosae maximum by using the filled function method as a global optimization technique.

In this study we applied the fuzzy logic approach in order to model the energy depending on the two torsion angles for the threonine (C4H9NO3) molecule. The model is set up according to theoretical results obtained by the density functional theory (B3LYP) with a 6-31 G(d) basic set on a Gausian program. We aimed to determine the best torsion angle values providing the energy of the molecule minimum by a fuzzy logic approach and to compare them with the density functional theory results. It was concluded that the fuzzy logic approach gives information about the untested data and its best value which are expensive and time-consuming to obtain by other methods and experimentation.

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