New hybrid conjugate gradient methods with the generalized Wolfe line search
1College of science, Nanjing University of Science and Technology, Nanjing, 210094 Jiangsu China.
Springerplus
|July 8, 2016
Summary
This study introduces two novel hybrid conjugate gradient methods, combining DY/HS and FR/PRP approaches for unconstrained optimization. These methods, utilizing a modified Wolfe line search, demonstrate descent and global convergence properties.
Area of Science:
- Numerical Analysis
- Optimization Theory
Background:
- Conjugate gradient methods are effective for unconstrained optimization.
- Existing methods like DY, HS, FR, and PRP have limitations.
Purpose of the Study:
- To develop new hybrid conjugate gradient methods.
- To enhance the performance and convergence of existing methods.
Main Methods:
- A linear combination of DY and HS methods was created.
- A linear combination of FR and PRP methods was developed.
- A modified Wolfe line search was employed to compute step sizes.
Main Results:
- The proposed hybrid methods exhibit descent properties.
- Global convergence properties for the hybrid methods were proven.
- The modified Wolfe line search ensures reliable step size computation.
Conclusions:
- The novel hybrid conjugate gradient methods offer improved performance.
- The integration with the modified Wolfe line search guarantees convergence.
- These methods provide a robust approach to unconstrained optimization problems.
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