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.
Highlights
1 Introduction The conjugate gradient (CG) methods have played an important role in solving nonlinear optimization problems due to their simplicity of iteration and very low memory requirements [1, 2]
The CG methods are not among the fastest or most robust optimization algorithms for solving nonlinear problems today, but they are very popular among engineers and mathematicians to solve nonlinear optimization problems [3,4,5]
We propose a q-variant of PRP method, called q-variant of the PRP (q-PRP), with the sufficient descent property independent of the line searches and convexity assumption of the objective function
Summary
The conjugate gradient (CG) methods have played an important role in solving nonlinear optimization problems due to their simplicity of iteration and very low memory requirements [1, 2]. In 2020, Yuan et al further proposed the PRP method and established the global convergence proof with the modified weak Wolfe–Powell line search technique for nonconvex functions. We utilize the q-gradient in inexact line search methods to generate the step-length which ensures the reduction of the objective function value.
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