On q-BFGS algorithm for unconstrained optimization problems

Abstract

Variants of the Newton method are very popular for solving unconstrained optimization problems. The study on global convergence of the BFGS method has also made good progress. The q-gradient reduces to its classical version when q approaches 1. In this paper, we propose a quantum-Broyden–Fletcher–Goldfarb–Shanno algorithm where the Hessian is constructed using the q-gradient and descent direction is found at each iteration. The algorithm presented in this paper is implemented by applying the independent parameter q in the Armijo–Wolfe conditions to compute the step length which guarantees that the objective function value decreases. The global convergence is established without the convexity assumption on the objective function. Further, the proposed method is verified by the numerical test problems and the results are depicted through the performance profiles.

Twin Support Vector Regression Model Based on Heteroscedastic Gaussian Noise and Its Application

“…In this experiment, we combined the optimization algorithm BFGS algorithm with ALM, and used BFGS algorithm in solving unconstrained sub-problems. BFGS algorithm shows good results in solving unconstrained subproblems, and many researchers have been optimizing this algorithm, such as Mishra et al [26].…”

Using the Hilfer–Katugampola fractional derivative in initial-value Mathieu fractional differential equations with application to a particle in the plane

“…During recent years, fractional Calculus draws increasing attention due to its applications in various applicable fields such as physics, mechanics, chemistry, engineering, etc. The reader interested in the subject should refer to the papers [1][2][3][4][5][6][7][8][9][10]. In the literature, one can find that there are many definitions of fractional derivatives [11][12][13][14][15].…”