Algorithms for minimization without derivatives

By R. Brent. 1974

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Citations in the corpus

Rosetta3: An Object-Oriented Software Suite for the Simulation and Design of Macromolecules (2011, positive): “…available line minimization algorithms are an inexact method using the Armijo backtracking acceptance criterion (Nocedal and Wright, 2006), a similar but “nonmonotone” method that allows the minimization trajectory to temporarily move uphill in energy, and a more exact method due to Brent (1973).”
Semi-Supervised Semantic Role Labeling (2009, methodology): “We optimized these parameters on the development set using Powell’s direction set method (Brent, 1973) with F1 as our loss function.”
Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation (2012, methodology): “This maximization can be accomplished numerically in a number of ways, for example by a derivative-free approximate Newton algo-rithm (49).”
Multilevel linear modelling for FMRI group analysis using Bayesian inference (2004, methodology): “To solve for ĥ using this equation, we use Brent’s (1973) algorithm.”
ROBUST HYPERPARAMETER ESTIMATION PROTECTS AGAINST HYPERVARIABLE GENES AND IMPROVES POWER TO DETECT DIFFERENTIAL EXPRESSION (2016, methodology): “Assuming that the dg are all equal, the hyperparameter d0 is estimated by equating s2z = φ(dg, d0) and solving for d0 using a modified Newton algorithm (Brent, 1973).”
A New Softmax Operator for Reinforcement Learning (2016, methodology): “In particular, in our experiments we used Brent’s method (Brent, 2013) available in python’s numpy library.”
Fast online deconvolution of calcium imaging data (2016, unknown): “We used Brent’s method [31] with bounds 0 ≤ γ < 1.”
Fine-mapping from summary data with the “Sum of Single Effects” model (2021, methodology): “To solve (17), we used the Brent-Dekker algorithm [46], which is implemented in R by the optimize function.”
Query Complexity of Derivative-Free Optimization (2012, methodology): “If the pairwise comparison oracle made no errors then the approximate line search is accomplished by a binary-search-like scheme, essentially a golden section line-search algorithm [25].”
A twist to partial least squares regression (2005, methodology): “A method based on so-called golden section search and parabolic interpolation, designed to search for a minimum of a one-variable function over a specified open interval, is described by Brent [13].”
Robust Demographic Inference from Genomic and SNP Data (2013, methodology): “The maximization of each parameter was done using Brent’s [80, Chapter 5] algorithm, which is a root-finding algorithm using a combination of bisection, secant and inverse quadratic interpolation [see e.g. 81].”
Applied Numerical Methods with MATLAB for Engineers and Scientists (2004, methodology): “2 Brent’s Method Algorithm The general idea behind the Brent’s root-finding method is whenever possible to use one of the quick open methods. In the event that these generate an unacceptable result (i.e., a root estimate that falls outside the bracket), the algorithm reverts to the more conservative”
Modern methods and algorithms of quantum chemistry (2000, background): “Summary of allocated global arrays ----------------------------------array 0 => double precision A(8,8), handle: -1000 (1:8,1:1) -> 0 (1:8,2:4) -> 1 (1:8,5:8) -> 2”
Discrete-time growth-dispersal models with shifting species ranges (2011, methodology): “…eigenvalue depends continuously on the parameters of the model, one can find the critical value for a parameter, such as c, corresponding to an important root, such as λ = 1, using a standard root-finding algorithm, such as the method of bisection or Brent’s method (Brent 1973; Press et al. 1992).”