A SURVEY OF NONLINEAR CONJUGATE GRADIENT METHODS

By William W. Hager, Hongchao Zhang. 2005

1,043 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5ea8516f807a88e4d768c926f6d7a5903796e76c

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Citations in the corpus

Forecasting exchange rate using deep belief networks and conjugate gradient method (2015, methodology): “Based on the survey carried by Wiliam and Zhang [24], a CG algorithm was presented by Hestenes and Stiefel in 1952, then several researchers proposed different approaches.”
Numerical Methods for Electronic Structure Calculations of Materials (2010, methodology): “Some of the best-performing NLCG methods today are hybrid methods [77].”
Two optimal Dai–Liao conjugate gradient methods (2015, methodology): “Different CG methods mainly correspond to different choices for the CG parameter for which a nice review has been presented in [1].”
A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinearequations (2011, methodology): “We refer to a survey paper [12] for a good review in the convergence property of the FR method and related conjugate gradient methods for optimization.”
Unifying Optimization Algorithms to Aid Software System Users: optimx for R (2011, background): “There is further work in this vein by Hager and Zhang (2006b) and Hager and Zhang (2006a) which remains to be investigated for its potential for use in R. Nash has coded the Dai/Yuan approach purely in R and added box constraints, yet the totality is no more complex than the existing CG…”
A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search (2013, background): “8 ) by Hager and Zhang [ 17 ] if s T k y k > 0 for all k .”
"Convex Until Proven Guilty": Dimension-Free Acceleration of Gradient Descent on Non-Convex Functions (2017, methodology): “In the first experiment, NCG required 2 function evaluations per step on average, indicating that its L1 estimate was stable for long durations.”
A scalable optimization approach for fitting canonical tensor decompositions (2011, background): “A treatment of preconditioning for NCG can be found in [23].”