A family of variable-metric methods derived by variational means

By Donald Goldfarb. 1970

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In Optimization & Training

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 & Mor´e, 1977), of which BFGS (Broy-den, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970) or LBFGS (Liu & Nocedal, 1989) are the most common choices.”
Entropy Search for Information-Efficient Global Optimization (2011, methodology): “…optimization algorithms: Trust-Region-Reﬂective (Coleman and Li, 1996, 1994), Active-Set (Powell, 1978b,a), interior point (Byrd et al., 1999, 2000; Waltz et al., 2006), and a na¨ıvely projected version of the BFGS algorithm (Broyden et al., 1965; 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.”
Randomized Quasi-Newton Updates Are Linearly Convergent Matrix Inversion Algorithms (2016, methodology): “The BFGS update [4, 10, 12, 34] can be seen as a projection of A−1 onto a space of rank-2 symmetric matrices.”
Does gold act as a hedge or a safe haven for stocks? A smooth transition approach (2014, unknown): “Thus we simultaneously estimate the following two equations by means of the BFGS numerical optimization method [Broyden, 1970; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970]: where r G,t and r S,t denote gold and stock returns, respectively, and ε t stands for a random error term.”
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).”
Pathfinder: Parallel quasi-Newton variational inference (2021, unknown): “The BFGS optimization algorithm is a quasi-Newton method that approximates the inverse Hessian through updates of positions and gradients of the objective function at positions along the optimization path (Broyden, 1970; Fletcher, 1987; Goldfarb, 1970; Shanno, 1970).”
Probabilistic Line Searches for Stochastic Optimization (2015, methodology): “It is a standard constituent of algorithms like the classic nonlinear conjugate gradient (Fletcher & Reeves, 1964) and BFGS (Broyden, 1969; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970) meth-ods (Nocedal & Wright, 1999, § 3).”