A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

Branch, Mary Ann; Coleman, Thomas F.; Li, Yuying

doi:10.1137/s1064827595289108

Cited by 793 publications

(510 citation statements)

References 11 publications

(13 reference statements)

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“…The experimental data for comparison has been extracted from Krier et al (2012). The density used in the calculations is N = 10 14 carriers/cm 3 Optimization Toolbox solvers is to restrict the trust-region subproblem to a two-dimensional subspace S (Branch et al 1999;Byrd et al 1988). Once the subspace S has been computed, the work to solve Eq.…”

Section: Numerical Methods and Resultsmentioning

confidence: 99%

Automated numerical characterization of dilute semiconductors per comparison with luminescence

Oriaku

Zubelli

et al. 2017

Opt Quant Electron

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This paper combines analytical approximations for the optical absorption and luminescence of semiconductors with trust region-reflective methods, delivering a robust numerical characterization method to be used in the study of new bulk semiconductors per direct comparison with experimental spectra. It further extends recent applications of the theory to the case of dilute nitride semiconductors and confirms results for the s-shape of the luminescence peak as a function of temperature.

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Section: Numerical Methods and Resultsmentioning

confidence: 99%

Automated numerical characterization of dilute semiconductors per comparison with luminescence

Oriaku

Zubelli

et al. 2017

Opt Quant Electron

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“…For each model, the best fit is obtained via the Trust Region Reflective ("trf") algorithm for optimization, well suited to efficiently explore the whole space of variables for a boundconstrained minimization problem (Branch et al 1999). In App.…”

Section: Fitting Methodsmentioning

confidence: 99%

Radio synchrotron spectra of star-forming galaxies

Klein

Lisenfeld

Verley

2018

A&A

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The radio continuum spectra of 14 star-forming galaxies are investigated by fitting nonthermal (synchrotron) and thermal (free-free) radiation laws. The underlying radio continuum measurements cover a frequency range of ∼325 MHz to 24.5 GHz (32 GHz in case of M 82). It turns out that most of these synchrotron spectra are not simple power-laws, but are best represented by a low-frequency spectrum with a mean slope α nth = 0.59 ± 0.20 (S ν ∝ ν −α ), and by a break or an exponential decline in the frequency range of 1 -12 GHz. Simple power-laws or mildly curved synchrotron spectra lead to unrealistically low thermal flux densities, and/or to strong deviations from the expected optically thin free-free spectra with slope α th = 0.10 in the fits. The break or cutoff energies are in the range of 1.5 -7 GeV. We briefly discuss the possible origin of such a cutoff or break. If the low-frequency spectra obtained here reflect the injection spectrum of cosmic-ray electrons, they comply with the mean spectral index of Galactic supernova remnants. A comparison of the fitted thermal flux densities with the (foreground-corrected) Hα fluxes yields the extinction, which increases with metallicity. The fraction of thermal emission is higher than believed hitherto, especially at high frequencies, and is highest in the dwarf galaxies of our sample, which we interpret in terms of a lack of containment in these low-mass systems, or a time effect caused by a very young starburst.

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“…In fact, the NLCO problem (20) only has three independent variables. Many optimisation methods in [5,24,26,[36][37][38][39][40][41][42][43][44][45][46] include the classical algorithms and intelligent algorithms such as Newton's method, quasi-Newton method, conjugate gradient method, convergent descent method, Lagrange method, interior point method, GA, immune algorithm and particle swarm algorithm that are often used to solve the optimisation problem. These methods are well established to solve the NLCO problem.…”

Section: Robust Optimal Controller Designmentioning

confidence: 99%

Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

et al. 2010

IET Control Theory &Amp; Applications

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Based on the new interval polynomial stability criterion and Lyapunov theorem, a robust optimal proportional -integral -derivative (PID) controller is proposed here to design for different plants that contain the perturbations of multiple parameters. A new stability criterion of the interval polynomial is presented to determine whether the interval polynomial belongs to Hurwitz polynomial. The robust optimal PID controller is acquired through minimising an augmented integral squared error (AISE) performance index. The robust optimal control problem is transformed into a non-linear constraint optimisation (NLCO) problem by applying new polynomial stability criterion and Lyapunov approach. The robust optimal PID parameters are obtained from solving the NLCO problem. The robustness and performances of the proposed method and other different tuning methods are compared. The ability of the proposed PID tuning method and other tuning methods to reject disturbances is discussed as well. The simulation results are presented to demonstrate the effectiveness of the proposed method and show better robustness of the robust optimal PID controller.

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A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

Cited by 793 publications

References 11 publications

Automated numerical characterization of dilute semiconductors per comparison with luminescence

Automated numerical characterization of dilute semiconductors per comparison with luminescence

Radio synchrotron spectra of star-forming galaxies

Design of robust optimal proportional–integral–derivative controller based on new interval polynomial stability criterion and Lyapunov theorem in the multiple parameters' perturbations circumstance

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