A HS-PRP-Type Hybrid Conjugate Gradient Method with Sufficient Descent Property

Area of Science:

• Numerical Analysis
• Optimization Theory

Background:

• Large-scale unconstrained optimization problems present significant computational challenges.
• Existing conjugate gradient (CG) methods have limitations in parameter generation and descent properties.

Purpose of the Study:

• To propose a new hybrid conjugate gradient (CG) method for large-scale unconstrained optimization.
• To ensure the proposed CG parameter is always nonnegative.
• To guarantee the search direction has sufficient descent properties independent of line search.

Main Methods:

• A hybrid approach combining the HS method and a modified PRP method.
• Utilizing the standard Wolfe-Powell line search rule for stepsize determination.
• Theoretical analysis to prove global convergence under standard assumptions.

Main Results:

• The proposed CG method generates a nonnegative CG parameter.
• The search direction is proven to have sufficient descent properties.
• Global convergence is established theoretically.
• Numerical results indicate the method is promising compared to existing techniques.

Conclusions:

• The developed hybrid CG method is effective for large-scale unconstrained optimization.
• The method offers improved properties such as nonnegative parameters and guaranteed descent.
• Further numerical evaluations suggest its potential as a valuable tool in optimization.