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Extension of Modified Polak‐Ribière‐Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems

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  • Zhifeng Dai

Abstract

Combining the Rosen gradient projection method with the two‐term Polak‐Ribière‐Polyak (PRP) conjugate gradient method, we propose a two‐term Polak‐Ribière‐Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1) search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2) the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio‐type line search. Preliminary numerical results show that the proposed method is promising.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:921364
    DOI: 10.1155/2014/921364
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    References listed on IDEAS

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    1. 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, Hindawi, vol. 2014, pages 1-12, January.
    2. Yuan-Yuan Chen & Shou-Qiang Du, 2013. "Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, March.
    3. Chuangxia Huang & Changlin Peng & Xiaohong Chen & Fenghua Wen, 2013. "Dynamics Analysis of a Class of Delayed Economic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Chuangxia Huang & Changlin Peng & Xiaohong Chen & Fenghua Wen, 2013. "Dynamics Analysis of a Class of Delayed Economic Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    5. Chuangxia Huang & Xu Gong & Xiaohong Chen & Fenghua Wen, 2013. "Measuring and Forecasting Volatility in Chinese Stock Market Using HAR‐CJ‐M Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Chuangxia Huang & Hanfeng Kuang & Xiaohong Chen & Fenghua Wen, 2013. "An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    7. Yuan-Yuan Chen & Shou-Qiang Du, 2013. "Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Chuangxia Huang & Xu Gong & Xiaohong Chen & Fenghua Wen, 2013. "Measuring and Forecasting Volatility in Chinese Stock Market Using HAR-CJ-M Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, March.
    9. 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).
    10. Chuangxia Huang & Hanfeng Kuang & Xiaohong Chen & Fenghua Wen, 2013. "An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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