A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems
Abstract
:1. Introduction
2. The Modified PRP Method and Its Properties
Algorithm 1 Modified PRPtype Conjugate Gradient Method 

3. Global Convergence of the ZPRP Method
 (i)
 The level set $\Omega =\{x\in {R}^{n}f\left(x\right)\le f\left({x}_{0}\right)\}$ is bounded.
 (ii)
 In some neighborhood N of $\Omega $, f is continuously differentiable and its gradient is Lipschitz continuous, that is, there exists a constant $L>0$ such that $\parallel g\left(x\right)g\left(y\right)\parallel \le L\parallel xy\parallel ,\forall x,y\in N$.
4. Extension to the HS and LS Method
5. Numerical Experiments
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Zheng, X.; Shi, J. A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems. Algorithms 2018, 11, 133. https://doi.org/10.3390/a11090133
Zheng X, Shi J. A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems. Algorithms. 2018; 11(9):133. https://doi.org/10.3390/a11090133
Chicago/Turabian StyleZheng, Xiuyun, and Jiarong Shi. 2018. "A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems" Algorithms 11, no. 9: 133. https://doi.org/10.3390/a11090133