A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search

By William W. Hager, Hongchao Zhang. SIAM Journal on Optimization, 2005

1,201 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/45efe38ea906de376db50a86b8a11ef566821e42

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Citations in the corpus

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition (2011, background): “This can be explained by loss of accuracy in checking the Wolfe sufficient decrease condition in the line search; see [13].”
A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search (2013, methodology): “8) by Hager and Zhang [17] if sk yk > 0 for all k.”
Two optimal Dai–Liao conjugate gradient methods (2015, methodology): “4) proposed by Hager and Zhang [5], and if we let (p, q) = (1, 0), then t p,q k reduces to the formula (1.”
The Variational Gaussian Approximation Revisited (2009, methodology): “c.archambeau@cs.ucl.ac.uk”
A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications (2019, methodology): “For examples, Xiao and Zhu [20] presented a CG method, which combines the well-known CG-DESCENT method in [17] and the projection method by Solodov and Svaiter [21].”
The cyclic Barzilai-–Borwein method for unconstrained optimization (2006, methodology): “In this subsection, we compare the performance of our adaptive cyclic BB stepsize algorithm, denoted ACBB, with the SPG2 algorithm of Birgin, Mart¶‡nez, and Raydan [5], with the PRP+ conjugate gradient code developed by Gilbert and Nocedal [24], and with the CG DESCENT code of Hager and Zhang [ 28 ,”
Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search (2006, methodology): “We test Algorithm 1 on problems in the CUTE [4] library and compare its performance with that of the steepest descent method, the standard FR method, the CG DESCENT method [15] and the PRP+ [13] method.”
A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence (2006, methodology): “We test almost all problems tested by Hager & Zhang (2005).”
Numerical optimization (2004, methodology): “See Dennis and Schnabel [92], Lemaréchal [189], Fletcher [101], Moré and Thuente [216] (in particular), and Hager and Zhang [161].”
On the best low multilinear rank approximation of higher-order tensors (2010, methodology): “To overcome this problem, an approximation of the Armijo condition was proposed in [ 36 ].”
A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints (2015, methodology): “To avoid solving the linear equations for obtaining the search direction at each step, Xiao and Zhu [19] developed a projected conjugate gradient method, which based on the projection technique in [14] and the CG-DESCENT method in [6], to solve the monotone nonlinear equations with convex constraint”