Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization. (2nd November 2017)

• Record Type: Journal Article
• Authors: Kobayashi, Hiroshi; Narushima, Yasushi; Yabe, Hiroshi
• Is Part Of: Optimization methods and software. Volume 32:Number 6(2017)
• Page Start: 1313
• Page End: 1329
• Publication Date: 2017-11-02
• Subjects: unconstrained optimization -- three-term conjugate gradient method -- secant condition -- sufficient descent property -- global convergence; 90C30 -- 90C06; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2017.1338288
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [ A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.