A novel modeling and smoothing technique in global optimization

Abstract

In this paper, we introduce a new methodology for modeling of the given data and finding the global optimum value of the model function. First, a new surface blending technique is offered by using Bezier curves and a smooth objective function is obtained with the help of this technique. Second, a new global optimization method followed by an adapted algorithm is presented to reach the global minimizer of the objective function. As an application of this new methodology, we consider energy conformation problem in Physical Chemistry as a very important real-world problem.

A new auxiliary function approach for inequality constrained global optimization problems

“…In order to obtain the global solution, any of the global optimization methods can be used. We use the auxiliary function based global optimization method studied in [21,33]. The Auxiliary Function Method (AFM) is very effective in terms of numerical results which is illustrated in [21].…”

“…We use the auxiliary function based global optimization method studied in [21,33]. The Auxiliary Function Method (AFM) is very effective in terms of numerical results which is illustrated in [21]. Our auxiliary function is defined as follows:φ…”

“…In recent years, the smoothing approaches have been used for many non-smooth problems such as minmax [15,16], exact penalty [17][18][19][20] and etc. [21].…”