Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Symmetrizing the Dai–Liao (DL) search direction matrix by a rank-one modification,  propose a one-parameter class of nonlinear conjugate gradient (CG) methods which includes the memoryless Broyden–Fletcher–Goldfarb–Shanno (MLBFGS) quasi-Newton updating formula. Then, conducting an eigenvalue analysis,  suggest two choices for the parameter of the proposed class of CG methods which simultaneously guarantee the descent property and ll-conditioning of the search direction matrix. A global convergence analysis is made for uniformly convex objective functions. Computational experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. Results of numerical comparisons made by the Dolan–More performance profile show that proper choices for the mentioned parameter may lead to promising computational performances.
['Saman Babaie-Kafaki', 'Reza Ghanbari']
I am writing a research paper on a idea Descent Symmetrization of the Dai–Liao Conjugate Gradient Method
[{"from": "human", "value": "I am writing a research paper on a idea Descent Symmetrization of the Dai\u2013Liao Conjugate Gradient Method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Symmetrizing the Dai\u2013Liao (DL) search direction matrix by a rank-one modification,  propose a one-parameter class of nonlinear conjugate gradient (CG) methods which includes the memoryless Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno (MLBFGS) quasi-Newton updating formula. Then, conducting an eigenvalue analysis,  suggest two choices for the parameter of the proposed class of CG methods which simultaneously guarantee the descent property and ll-conditioning of the search direction matrix. A global convergence analysis is made for uniformly convex objective functions. Computational experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. Results of numerical comparisons made by the Dolan\u2013More performance profile show that proper choices for the mentioned parameter may lead to promising computational performances."}]