Newton Like Line Search Method Using q-Calculus

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

“…A modified least mean algorithm using q-calculus was also proposed which automatically adapted the learning rate with respect to the error and was shown to have fast convergence [36]. In optimization, the q-calculus was employed in Newton, modified Newton, BFGS, and limited memory BFGS methods for solving unconstrained nonlinear optimization problems [19,[37][38][39][40] with the least number of iterations. In the field of conjugate gradient methods, the q-analogue of the Fletcher-Reeves method was developed [41] to optimize unimodal and multimodal functions, and the Gaussian perturbations were used in some iterations to ensure the convergence globally in the probabilistic sense only.…”

A q-Gradient Descent Algorithm with Quasi-Fejér Convergence for Unconstrained Optimization Problems

“…However, the convergence properties of the steepest descent method with inexact line searches have been studied under several strategies for the choice of the step length α k [36][37][38]. Recently, several modified unconstrained optimization algorithms using the q-gradient have been proposed to solve unconstrained optimization problems [10,19,[39][40][41].…”

On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

“…Further, global optimum was searched using q-steepest descent method and q-conjugate gradient method where a descent scheme is presented using q-calculus with the stochastic approach which does not focus on the order of convergence of the scheme [33]. The q-calculus is applied in Newton's method to solve unconstrained single objective optimization [34]. Further, this idea is extended to solve (UMOP) within the context of the q-calculus [35].…”