A q-spectral Polak-Ribiére-Polyak conjugate gradient method for unconstrained optimization problems with motion control application

Frank Hilton Jackson extended the classical concept of derivative and introduced the qderivative, popularly known as Jackson’s derivative. To solve large-scale unconstrained optimization problems, we propose a q-spectral Polak-Ribiére-Polyak (PRP) conjugate gradient method. The method can be viewed as a generalization of the spectral PRP method, replacing the classical gradient with the q-gradient vector that utilises the first-order partial q-derivatives derived from Jackson’s derivative. Additionally, as the value of q approaches one, the proposed approach simplifies to the classical form. Numerical experiments are conducted and compared with existing methods to demonstrate the advantages of the proposed approach. Moreover, as an application, we solve the motion control problem.