## Abstract and Applied Analysis

### A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

#### 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 $\gamma$ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 386030, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277002

Digital Object Identifier
doi:10.1155/2014/386030

Mathematical Reviews number (MathSciNet)
MR3214429

Zentralblatt MATH identifier
07022283

#### Citation

Sun, Min; Liu, Jing. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate. Abstr. Appl. Anal. 2014 (2014), Article ID 386030, 6 pages. doi:10.1155/2014/386030. https://projecteuclid.org/euclid.aaa/1412277002

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