On q-BFGS algorithm for unconstrained optimization problems

Advances in Difference Equations

Bhagwat Ram¹  Shashi Kant Mishra²  Mohammad Esmael Samei³  Geetanjali Panda⁴  Suvra Kanti Chakraborty⁵ 

[1] DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, 221005, Varanasi, India;Department of Mathematics, Banaras Hindu University, 221005, Varanasi, India;Department of Mathematics, Bu-Ali Sina University, 65178, Hamedan, Iran;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India;Department of Mathematics, Sir Gurudas Mahavidyalaya, 700067, Kolkata, India;

关键词: Unconstrained optimization;    BFGS method;    q;    Global convergence;    90C30;    65K05;    05A40;   

DOI  :  10.1186/s13662-020-03100-2

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY