2019
DOI: 10.1137/1.9781611975604
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Practical Optimization

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Cited by 406 publications
(434 citation statements)
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“…In the MCR-BANDS method, 18 the optimization (maximum and minimum) of the function given by Equation 11 under constraints is performed using a nonlinear constrained nonlinear optimization problem, based on a sequential quadratic programming algorithm implemented in the MATLAB optimization toolbox fmincon function. 21 The above optimization procedure produces 2 important outputs: (1) the profiles of every component in the 2 modes corresponding to the maximum, f n,max , and minimum, f n,min , contribution to the whole signal, which can be plotted for visual inspection; and (2) the difference between the maximum and minimum (f n,max − f n,min ) of the component contribution (scaled between 0 and 1), which gives a measure of the extension of rotational ambiguity associated to this component. A value of 0 means no rotational ambiguity, while a value close to 1 corresponds to total ambiguity for this component.…”
Section: Methodsmentioning
confidence: 99%
“…In the MCR-BANDS method, 18 the optimization (maximum and minimum) of the function given by Equation 11 under constraints is performed using a nonlinear constrained nonlinear optimization problem, based on a sequential quadratic programming algorithm implemented in the MATLAB optimization toolbox fmincon function. 21 The above optimization procedure produces 2 important outputs: (1) the profiles of every component in the 2 modes corresponding to the maximum, f n,max , and minimum, f n,min , contribution to the whole signal, which can be plotted for visual inspection; and (2) the difference between the maximum and minimum (f n,max − f n,min ) of the component contribution (scaled between 0 and 1), which gives a measure of the extension of rotational ambiguity associated to this component. A value of 0 means no rotational ambiguity, while a value close to 1 corresponds to total ambiguity for this component.…”
Section: Methodsmentioning
confidence: 99%
“…The computational experiment for each of the structures consisted of sequential search for E estimated with condition (1) for all possible pairs of the structures in the set. In algorithm 3, at each iteration of the coordinate-wise descent, the minimum was determined by the golden section method (Gill et al, 1981). For S 1 the strict value E exact was calculated using the Kabsch algorithm for all 9!…”
Section: Results Of Numerical Experimentsmentioning
confidence: 99%
“…For the ML estimation of κ , we insert the theoretical signal model defined in equation in the place of Φ ss ( ω k ; θ ), as well as an estimate truenormalΦ^wwfalse(ωfalse) of the noise PSD, and solve maxbold-italicθ0.3emscriptLfalse(boldx;bold-italicθfalse), by using measurements from a suitably selected frequency range [ ω 1 , ω 2 ]. Although in our case the maximization of scriptLfalse(boldx;bold-italicθfalse) cannot be achieved analytically, the existence of gradient information for the likelihood function enables the use of fast and accurate methods such as the quasi‐Newton or the trust‐region algorithms (Gill et al, ) for the numerical solution of , starting from an initial guess θ (0) =[ κ (0) , C (0) ] T of the unknown parameter values.…”
Section: Maximum Likelihood Based κ Estimationmentioning
confidence: 99%