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

Abstract

In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations.

New Hybrid Conjugate Gradient Method with Global Convergence Properties under Exact Line Search

“…Thirty-one unconstrained optimization test problems are taken from [22] and fully listed in Table 1. We analyze the efficiency of our new formula by comparing its numerical performance with the FR [2], PRP [3,4], WYL [21] and HRM3 [23] methods. All of the tested CG algorithms use as the stopping criterion with as suggested by [24].…”

A new hyhbrid coefficient of conjugate gradient method

“…Due to their simple approach, CG methods in (7) - (14) are said to be classical. Detailed discussions are available in [13][14][15][16][17][18][19][20][21][22][23][24].…”

A Robust Spectral Three-Term Conjugate Gradient Algorithm for Solving Unconstrained Minimization Problems

“…The researchers (Hamoda, Rivaie and Mamat) in [15] have developed another new CG-type formula for the formulas mentioned in the above table by changing the compound based on the convex structure method to obtain better results compared to the previous formulas by suggesting the following formula:…”

“…Then from the results that obtained by [15], the quantity of the parameter u=0.9 i.e. ∈ (0,1) and from given in equation 8, the search direction of this formula was given in the following gradient:…”

“…[32] introduced an odd plan of its predecessors from the formulas of the PR-CG methodology referred to as the WYL-CG methodology. Zhang recommended through his study a lot of and has improved WYL-CG normal methodology victimization the new CG, additionally it well-tried that the strategy of NPR-CG met the traditional demand ratios beneath conditions of line search SWP [15]. Finally, Zhang et al planned another changed CG-method referred to as the MPR-CG methodology, wherever Dai and Wen [31] planned another changed version of NPR-CG methodology referred to as the DPR-CG methodology.…”