A modified nonlinear conjugate gradient method for unconstrained optimization

Abstract

Nonlinear conjugate gradient method holds an important role in solving large scale unconstrained optimization problems. Their simplicity, low memory requirement, and global convergence stimulated a massive study on the method. Numerous modifications have been done recently to improve its performance. In this paper, we proposed a new formula for the conjugate gradient coefficient k  that generates the descent search direction. In addition, we establish the global convergence result under exact line search. The outcome of our numerical experiment show that the proposed formula is very efficient and more reliable when compare to other conjugate gradient methods.

A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization

“…During the last decade, much effort has been devoted to developing new modifications of conjugate gradient methods which do not only possess strong convergence properties, but they are also computationally superior to the classical methods. Such methods can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

A Modified Wei-Yao-Liu Conjugate Gradient Method for Unconstrained Optimization and Motion Control of Robotic Motion Manipulators

“…However, the methods presented in (7) are influenced by jamming phenomena which affects their computational performance [16,21]. The convergence issues from the first set of CG methods defined in (6) and the poor numerical results from the second set (7) has led to numerous studies of the CG formulas [16,[22][23][24][25][26][27][28][29][30][31][32].…”

Convergence analysis of a new conjugate gradient method for unconstrained optimization

“…Among them, a modified Fletcher-Reeves and Conjugate descent CG methods were presented in [17], a modified Hestenes-Stiefel CG method proposed in [18], a modified Poyak-Rebiere-Polak CG method in [19],and a modified Liu-Storey nonlinear CG method was presented in [13]. Also refer to [21,22,23,24] for some recent researches on the properties of CG methods.…”