A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

Journal of Inequalities and Applications

Bhagwat Ram¹  Mohammad Esmael Samei²  Shashi Kant Mishra³  Suvra Kanti Chakraborty⁴ 

[1] DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University;Department of Mathematics, Bu-Ali Sina University;Department of Mathematics, Institute of Science, Banaras Hindu University;Department of Mathematics, Sir Gurudas Mahavidyalaya;

关键词: Unconstrained optimization;    Conjugate gradient method;    Global convergence;    q-calculus;   

DOI  :  10.1186/s13660-021-02554-6

来源: DOAJ

【 摘 要 】

Abstract A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

【 授权许可】

Unknown