On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

Coleman, Thomas F.; Li, Yuying

doi:10.1007/bf01582221

Cited by 1,061 publications

(602 citation statements)

References 18 publications

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“…It was decided to do all curve-fitting with MATLAB's lsqcurvefit function, which is based on the interiorreflective Newton method described in Ref (21,22) This approach was reliable for all models using the following fitting parameters: tolerance ("TolFun") 10 -12 , maximum number of iterations ("MaxIter") 2000, maximum function evaluations ("MaxFunEvals") 10000, maximum preconditioned conjugate gradient iterations ("MaxPCGIter") 1. Bound constraints 1/5000 ≤ μ j ≤ 1/50 and 1/500 ≤ ν j , ν sys ≤ 5 were used to prevent μ j → ∞ or ν j → ∞ , which remained problematic for the optimization algorithm (since the fitted signal became zero before the first data point).…”

Section: Discussionmentioning

confidence: 99%

Relaxation effects in the quantification of fat using gradient echo imaging

Bydder

Yokoo

Hamilton

et al. 2008

Magnetic Resonance Imaging

360

577

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Quantification of fat has been investigated using images acquired from multiple gradient echos. The evolution of the signal with echo time and flip angle was measured in phantoms of known fat and water composition and in 21 research subjects with fatty liver. Data were compared to different models of the signal equation, in which each model makes different assumptions about the T1 and/ or T2* relaxation effects. A range of T1, T2*, fat fraction and number of echos was investigated to cover situations of relevance to clinical imaging. Results indicate that quantification is most accurate at low flip angles (to minimize T1 effects) with a small number of echos (to minimize spectral broadening effects). At short echo times the spectral broadening effects manifest as a short apparent T2 for the fat component.

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Section: Discussionmentioning

confidence: 99%

Relaxation effects in the quantification of fat using gradient echo imaging

Bydder

Yokoo

Hamilton

et al. 2008

Magnetic Resonance Imaging

360

577

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“…[8] and [9]: [27] is attained. In the present article, a nonlinear least-squares optimization algorithm, known as the trust-region-reflective algorithm, [57,58] was applied. In order to reduce dispersive errors of de p appearing due to complex loading and, consequently, yielding on a discrete grid, the Savitzky-Golay filter [59] was applied on a temporally overlaid de p signal.…”

Section: ½23mentioning

confidence: 99%

Heat Transfer Coefficient at Cast-Mold Interface During Centrifugal Casting: Calculation of Air Gap

Boháček

Kharicha

Ludwig

et al. 2018

Metall Mater Trans B

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During centrifugal casting, the thermal resistance at the cast-mold interface represents a main blockage mechanism for heat transfer. In addition to the refractory coating, an air gap begins to form due to the shrinkage of the casting and the mold expansion, under the continuous influence of strong centrifugal forces. Here, the heat transfer coefficient at the cast-mold interface h has been determined from calculations of the air gap thickness d a based on a plane stress model taking into account thermoelastic stresses, centrifugal forces, plastic deformations, and a temperature-dependent Young's modulus. The numerical approach proposed here is rather novel and tries to offer an alternative to the empirical formulas usually used in numerical simulations for a description of a time-dependent heat transfer coefficient h. Several numerical tests were performed for different coating thicknesses d C , rotation rates X, and temperatures of solidus T sol . Results demonstrated that the scenario at the interface is unique for each set of parameters, hindering the possibility of employing empirical formulas without a preceding experiment being performed. Initial values of h are simply equivalent to the ratio of the coating thermal conductivity and its thickness (~1000 Wm À2 K À1 ). Later, when the air gap is formed, h drops exponentially to values at least one order of magnitude smaller (~100 Wm À2 K À1 ).

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“…From Equation (12), the number of failures in each interval is given by (20) can then be written in matrix form as: Since Q is highly non-linear, the above minimum is solved by a large-scale algorithm which is a subspace trust region method and is based on the interior-reflective Newton method [15] [16] . With the values  and , by equations (19) and (24) an estimate for the parameter  can be obtained.…”

Section: Least Squares Estimatesmentioning

confidence: 99%