Abstract
Theconjugate gradient method is widely used to solve large scale unconstrainedoptimization problems. However, the rate of convergence conjugate gradient method is linearunless it restarted. In this study, we present a new spectral conjugategradient modification formula with restart property obtains the globalconvergence and descent properties.In addition, we proposed a new restart condition for Fletcher-Reeves conjugate gradient formula. The numerical resultsdemonstrated that the modified Fletcher-Reeves parameter and the new CG formulawith their restart conditions are more efficient and robustness than otherconventional methods.
Highlights
We consider the following problem: min f (x), x Rn, (1)where, f: Rn R is continuous and differentiable function and its gradient g(x) = f(x) is available
1, k dk where, gk = g(xk) and k is known as the conjugate gradient parameter
If the step length is defined such that the search direction minimized i.e., this line search is called exact line search where this line search is expensive
Summary
Polak and Ribière (1969) proved CG method with the PRP formula and by using exact line search is convergent. 0, Zoutendijk (1970) obtain the global convergence of FR formula with CG method and the exact line search. As we know that in the case of the function is quadratic i.e., f(x) = gTx+(1/2)xTHx and the step size obtained by exact line search (3), the CG method satisfy the conjugacy condition i.e., d. Hager and Zhang (2005; 2013) presented a modified CG parameter that satisfies the descent property for any inexact line search with gkTdk 7 / 8 gk 2. This formula is given as follows: HZ k. T k dk min , gk and > 0 is a constant
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
