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

A Polak-Ribiere-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.

Automated summary

The paper introduces a q-variant of the PRP method for solving nonlinear unconstrained optimization problems, which satisfies both sufficient and conjugacy conditions at every iteration. The method is globally convergent with standard and strong Wolfe conditions, showing promising results in numerical tests with different starting points. Additionally, as the parameter q approaches 1, the method reduces to the classical PRP method.