Variance algorithm for minimization

Davidon, William C.

doi:10.1093/comjnl/10.4.406

Cited by 487 publications

(83 citation statements)

References 4 publications

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“…In the output file (see Appendix B) the result array is saved as an ASCII vector; 2. The basic idea of the Davidon Variance Algorithm (Davidon 1968) is to calculate the covariance matrix by an iterative algorithm. The matrix is obtained by using only the function values and the gradient, and the minimum value is calculated simultaneously as the algorithm converges.…”

Section: Minimizing the Negative Log-likelihood Functionmentioning

confidence: 99%

SNOC: A Monte-Carlo simulation package for high-zsupernova observations

Goobar

Mörtsell

Amanullah

et al. 2002

A&A

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Abstract. We present a Monte-Carlo package for simulation of high-redshift supernova data, SNOC. Optical and near-infrared photons from supernovae are ray-traced over cosmological distances from the simulated host galaxy to the observer at Earth. The distances to the sources are calculated from user provided cosmological parameters in a Friedmann-Lemaître universe, allowing for arbitrary forms of "dark energy". The code takes into account gravitational interactions (lensing) and extinction by dust, both in the host galaxy and in the line-of-sight. The user can also choose to include exotic effects like a hypothetical attenuation due to photon-axion oscillations. SNOC is primarily useful for estimations of cosmological parameter uncertainties from studies of apparent brightness of type Ia supernovae vs redshift, with special emphasis on potential systematic effects. It can also be used to compute standard cosmological quantities like luminosity distance, lookback time and age of the universe in any Friedmann-Lemaître model with or without quintessence.

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Section: Minimizing the Negative Log-likelihood Functionmentioning

confidence: 99%

SNOC: A Monte-Carlo simulation package for high-zsupernova observations

Goobar

Mörtsell

Amanullah

et al. 2002

A&A

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“…Although they generally need more iterations to achieve convergence than the Newton method, their numerical efficiency means that they are usually faster and, furthermore, tend to be more robust to the condition of the model and data. The OPTMUM procedure contains three such algorithms: the BFGS method due to Broyden (1967), Fletcher (1970), Goldfarb (1970) and Shanno (1970), the DFP method of Davidon (1968) and Fletcher and Powell (1963), and BFGS-SC, which is a modified BFGS algorithm in which the formula for the computation of the update of the Hessian estimate has been changed to make it scale free. In all three cases, the OPTMUM implementation of the algorithm uses the Cholesky factorization of the approximation to the Hessian in (3.3), i.e., H = C 0 C, before solution for d. The BFGS algorithm is the default choice in OPTMUM, while the other five are available as options.…”

Section: Nonlinear Optimizationmentioning

confidence: 99%

Investigating Nonlinearity: A Note on the Estimation of Hamilton's Random Field Regression Model

Bond¹,

Harrison²,

O’Brien³

2005

Studies in Nonlinear Dynamics &Amp; Econometrics

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This is a revised and extended version of the authors' 2003 Trinity Economic Paper. It describes Hamilton's (2001) approach to nonlinear econometric modelling and some of the methods of nonlinear optimization, as before, but adds significantly to the investigation of Hamilton's Gauss program for the implementation of his methodology. Specifically, it reports on the performance of this program using data relating to Hamilton's US Phillips curve example, the use of two versions of the Gauss software and a range of numerical optimization options. It also examines the impact of changes in initial parameter estimates, the use of algorithm switching strategies, and the effects of changes in the sample data on the results produced by Hamilton's procedure. The new results presented suggest some further clear conclusions that will be of value to those using Hamilton's method.J.E.L. Classification: C13, C51, C61

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“…O {hi (2)(3)(4)(5)(6)(7)(8)(9)(10)(11) If IV indicates the set of points at which violation of the jth type of constraint occur, then the 0 operator solves a "'local" optimization problem at the highest point, hn, in the set Ij. The optimization problem is to minimize…”

Section: {Yi)mentioning

confidence: 99%

“…{hi}O = {Ti + Snin) (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) Greaves works with zero minimum clearance, but it is trivial to extend the procedure to non-zero values. The clearance constraint that the final set of points must satisfy is yi -Ti + cmi (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) and is maintained during each iteration step by the "non-lowering" requirement:…”

Section: {Yi)mentioning

confidence: 99%

Terrain Following Control Based on an Optimized Spline Model of Aircraft Motion

Funk¹

1975

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Variance algorithm for minimization

Cited by 487 publications

References 4 publications

SNOC: A Monte-Carlo simulation package for high-zsupernova observations

SNOC: A Monte-Carlo simulation package for high-zsupernova observations

Investigating Nonlinearity: A Note on the Estimation of Hamilton's Random Field Regression Model

Terrain Following Control Based on an Optimized Spline Model of Aircraft Motion

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