On a new smoothing technique for non-smooth, non-convex optimization

Abstract

In many global optimization techniques, the local search methods are used for different issues such as to obtain a new initial point and to find the local solution rapidly. Most of these local search methods base on the smoothness of the problem. In this study, we propose a new smoothing approach in order to smooth out non-smooth and non-Lipschitz functions playing a very important role in global optimization problems. We illustrate our smoothing approach on well-known test problems in the literature. The numerical results show the efficiency of our method.

A New Smoothing Algorithm to Solve a System of Nonlinear Inequalities

“…Smoothing functions have been studied by many scholars [21][22][23][24] and they have been applied to solve many interesting nonsmooth problems over the years [25][26][27]. The comprehensive overview on smoothing approaches can be found in [20,28,29].…”

An exact penalty function approach for inequality constrained optimization problems based on a new smoothing technique

“…R + represents the non-negative real numbers. Smoothing functions are often used to solve non-smooth optimization problems [9][10][11][12]. In addition, there is quite a lot of work in the literature on smoothed penalty functions l 1 and l p [13][14][15][16][17][18][19][20].…”

Generalization of hyperbolic smoothing approach for non-smooth and non-Lipschitz functions

“…Therefore, many interesting non-smooth problems have been solved by using smoothing functions such as min-max [45], sum-max [36], penalty expressions of constrained optimization problems [19] and regularization problems [37,14,21]. Many interesting algorithms are developed and they are effectively applied to the nonsmooth optimization problems [44]. On the other hand, not only are the smoothing techniques used for non-differentiable optimization problems but they are also applicable for solving system of equations/inequalities [46] including absolute value equations [7], many different versions of complementarity problems [29] and etc.…”