The Convergent Properties of a New Parameter for Unconstrained Optimization

Abstract

Because of its simplicity, low memory requirement, low computational cost, and global convergence properties, the Conjugate Gradient (CG) method is the most popular iterative mathematical technique for optimizing both linear and nonlinear systems. Some classical CG methods, however, have drawbacks such as poor global convergence and numerical performance in terms of iterations and function evaluations. To address these shortcomings, researchers proposed new CG parameter variants with efficient numerical results and good convergence properties. We present a new conjugate gradient formula  based on the memoryless self-scale DFP quasi-Newton (QN) method in this paper. The proposed new formula fulfills the sufficient descent property and the global convergent condition with any proposed line research. When the exact line search is used, the proposed formula is reduced to the classical HS formula. Finally, we conclude that our proposed method is effective.