The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
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8,059 citations
Cites background from "The Barzilai and Borwein Gradient M..."
...This is known as the Barzilai-Borwein (BB) or spectral stepsize (Barzilai and Borwein 1988; Fletcher 2005; Raydan 1997)....
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982 citations
Additional excerpts
...Work sponsored by FAPESP, FAEP-UNICAMP and CDCH-UCV....
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Cites background or result from "The Barzilai and Borwein Gradient M..."
...Many subsequent papers, such as [2, 6, 8, 11, 15, 18], have exploited nonmonotone line search techniques of this nature....
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...Second, in some cases, the numerical performance is very dependent on the choice of M (see [7, 15, 16])....
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...Encouraging numerical results have been reported [6, 8, 11, 14, 15, 16] when nonmonotone schemes were applied to difficult nonlinear problems....
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503 citations
References
7,278 citations
"The Barzilai and Borwein Gradient M..." refers background in this paper
...For a complete discussion on this topic see [3], [4], and [14]....
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6,217 citations
"The Barzilai and Borwein Gradient M..." refers background in this paper
...For a complete discussion on this topic see [3], [4], and [14]....
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2,585 citations
"The Barzilai and Borwein Gradient M..." refers background in this paper
...Barzilai and Borwein [1] presented a convergence analysis in the two-dimensional quadratic case....
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...In fact, Barzilai and Borwein [1] observed that this new choice of steplength required less computational work and greatly speeded up the convergence of the gradient method for quadratics....
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