A new modified scaled conjugate gradient method for large-scale unconstrained optimization with non-convex objective function. (4th July 2019)

• Record Type: Journal Article
• Authors: Khoshgam, Zahra; Ashrafi, Ali
• Is Part Of: Optimization methods and software. Volume 34:Number 4(2019)
• Page Start: 783
• Page End: 796
• Publication Date: 2019-07-04
• Subjects: secant equation -- conjugate gradient method -- memoryless BFGS method -- large scale -- unconstrained optimization problems; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1457152
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, according to the fifth-order Taylor expansion of the objective function and the modified secant equation suggested by Li and Fukushima, a new modified secant equation is presented. Also, a new modification of the scaled memoryless BFGS preconditioned conjugate gradient algorithm is suggested which is the idea to compute the scaling parameter based on a two-point approximation of our new modified secant equation. A remarkable feature of the proposed method is that it possesses a globally convergent even without convexity assumption on the objective function. Numerical results show that the proposed new modification of scaled conjugate gradient is efficient.