Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy
Predrag S. Stanimirović, Branislav Ivanov, Dragiša Stanujkić, Vasilios N. Katsikis, Spyridon D. Mourtas, Lev Kazakovtsev, S. A. Edalatpanah
Abstract
The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods.