A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate. (19th May 2014)

• Record Type: Journal Article
• Authors: Sun, Min; Liu, Jing
• Other Names: Danilov Vladimir Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-05-19
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/386030
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.