Fuzzy Adaptive Parameter in the Dai–Liao Optimization Method Based on Neutrosophy

Abstract

The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, we suggest and explore a new neutrosophic logic system intended to compute the essential parameter t required in Dai–Liao CG iterations. Theoretical examination and numerical experiments signify the effectiveness of the introduced method for controlling t. By incorporation of the neutrosophy in the Dai–Liao conjugate gradient principle, we established novel Dai–Liao CG iterations for solving large-scale unconstrained optimization problems. Global convergence is proved under standard assumptions and with the use of the inexact line search. Finally, computational evidence shows the computational effectiveness of the proposed fuzzy neutrosophic Dai–Liao CG method.

Keywords

• neutrosophic logic systems
• Dai–Liao conjugate gradient method
• backtracking line search
• convergence
• unconstrained optimization