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Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

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  • San-Yang Liu
  • Yuan-Yuan Huang
  • Hong-Wei Jiao

Abstract

Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large‐scale nonsmooth equations.

Suggested Citation

  • San-Yang Liu & Yuan-Yuan Huang & Hong-Wei Jiao, 2014. "Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:305643
    DOI: 10.1155/2014/305643
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    References listed on IDEAS

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    1. Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
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    Cited by:

    1. Zhifeng Dai, 2014. "Extension of Modified Polak‐Ribière‐Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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