Quantum Fletcher Reeves Conjugate Gradient Method

Numerous applications involve optimization problems, including image processing (Hassan Ibrahim et al. 2020), science (Lin et al. 2020a) and engineering (Hubmer et al. 2020; Lin and Jiang 2020b), solving M-tensor equations (Liu et al. 2020c; Fukushima 1990), etc. It is crucial to create efficient solutions for these issues. Large-scale unconstrained optimization problems can be quickly and accurately solved using gradient-based descent algorithms like conjugate gradient (Fukushima 1990; Mishra and Ram 2019a), Newton (Mishra and Ram 2019b), quasi-Newton (Mishra and Ram 2019c), and steepest descent (Mishra and Ram 2019d). First-order techniques that only require the gradient of the objective function in each iteration are the conjugate gradient descent and steepest descent techniques.The Newton and quasi-Newton techniques, on the other hand, are second-order methods that need the objective function’s gradient and Hessian in each iteration.