Quantum Broyden Fletcher Goldfarb Shanno Method

Several optimization methods have been developed extensively for solving unconstrained optimization problems. The gradient descent method is one of the most simplest and commonly used method in the field of the optimization (Mishra and Ram 2019a). This method is globally convergent, but suffers from the slow convergence rate as the iterative point approaches to minimum point. In order to improve the convergence rate, optimizers use the Newton method (Mishra and Ram 2019b). This method is one of the most popular method for its quadratic convergence. A major disadvantage of Newton method is its non-convergence or slowness for the starting point not being chosen close to the minimum point, and it also requires to compute the inverse of the Hessian at every iteration that is rather costly. The components of the Hessian matrix are constructed using classical derivative, which is positive definite at every iteration. In quasi-Newton methods, instead of computing the actual Hessian, an approximation of the Hessian is considered (Mishra and Ram 2019c). These methods use only first derivatives to make an approximation whose computing costs are low.