The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm

By C. G. Broyden. 1970

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Citations in the corpus

Fast large-scale optimization by unifying stochastic gradient and quasi-Newton methods (2013, methodology): “The first is to use a quasi-Newton method (Dennis Jr & Moré, 1977), of which BFGS (Broyden, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970) or LBFGS (Liu & Nocedal, 1989) are the most common choices.”
The Case for Full-Matrix Adaptive Regularization (2018, methodology): “Our algorithm bears a superﬁcial resemblance to L-BFGS [LN89], a version of BFGS [Bro70, Fle70, Gol70, Sha70] which uses a sliding window of gradient history.”
Benchmarking the BFGS algorithm on the BBOB-2009 function testbed (2009, methodology): “The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [1, 3, 4, 7] is a real-parameter unconstrained non-linear optimization method.”
Newton-Stein Method: An Optimization Method for GLMs via Stein's Lemma (2015, methodology): “A well-known member of this class of algorithms is the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (Broyden, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970).”
Convergence Properties of the BFGS Algoritm (2002, methodology): “The BFGS algorithm is one of the most e(cid:14)cient quasi-Newton methods for unconstrained optimization: The algorithm was proposed by Broyden [2], Fletcher [5], Goldfarb [7], and Shanno [19] individually and can be stated as follows.”
Robust min}max portfolio strategies for rival forecast and risk scenarios (2000, methodology): “HK k is evaluated using Powell's (1978) modi"cation to the BFGS quasiNewton formula (Broyden, 1969, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970).”
The Gravity Model for International Trade: Specification and Estimation Issues (2015, unknown): “The first-order condition for the NBPML estimator has been solved using the optim() function in R, with the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno algorithm (see Broyden, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970).”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, methodology): “BFGS Broyden, Fletcher, Goldfarb and Shanno proposed the BFGS method [135], [136], [137], [3], in which Bt+1 is updated according to”