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

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  • Min Sun
  • Jing Liu

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.

Suggested Citation

  • Min Sun & Jing Liu, 2014. "A Globally Convergent Matrix‐Free Method for Constrained Equations and Its Linear Convergence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:386030
    DOI: 10.1155/2014/386030
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    References listed on IDEAS

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    1. Eberhard Zeidler, 1990. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-0981-2, March.
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