Second derivative Gauss-Newton-based method for solving nonlinear simultaneous equations

Dimmer, P.R.; Cutteridge, O.P.D.

doi:10.1049/ip-g-1.1980.0047

Cited by 3 publications

(2 citation statements)

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“…This algorithm [6] is from the same family as the Levenberg-Marquardt. It minimize the error of output by varying w using step size  ) (…”

Section: Gauss-newton (Gn) Algorithmmentioning

confidence: 99%

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell

Dkhichi¹,

Oukarfi²

2014

IJIRSET

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This present paper deals with the parameter determination of solar cell by using an artificial neural network trained at every time, separately, by one algorithm among the optimization algorithms of gradient descent (Levenberg-Marquardt, Gauss-Newton, Quasi-Newton, steepest descent and conjugate gradient). This determination issue is made for different values of temperature and irradiance. The training process is insured by the minimization of the error generated at the network output. Therefore, from the outcomes obtained by each gradient descent algorithm, we conducted a comparative study between the overall of training algorithms in order to know which one had the best performances. As a result the Levenberg-Marquardt algorithm presents the best potential compared to the other investigated optimization algorithms of gradient descent.

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“…This algorithm [6] is from the same family as the Levenberg-Marquardt. It minimize the error of output by varying w using step size  ) (…”

Section: Gauss-newton (Gn) Algorithmmentioning

confidence: 99%

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell

Dkhichi¹,

Oukarfi²

2014

IJIRSET

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“…Dimmer and Cutteridge [4] described a a transistor modelling problem which was studied by many others [15,17]. This problem reduces to minimising a sum of squares involving a set of nine dimensional nonlinear equations.…”

Section: Transistor Design Problemmentioning

confidence: 99%

TAM-EDA: Multivariate t Distribution, Archive and Mutation Based Estimation of Distribution Algorithm

Gao¹,

Wood

2014

ANZIAMJ

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We present a novel estimation of a distribution algorithm (eda), tam-eda, which uses a multivariate t distribution model, an archive population and a mutation operation to escape local minima, avoid premature convergence and utilize a record of the best solutions. Earlier edas used multivariate normal distributions to model low-cost regions of the search space. The multivariate t distribution has heavier tails and so is more likely to maintain diversity, while still allowing convergence to occur. The current population of potential solutions has limited ability to represent all the best regions of the search space explored so far. The archive allows storage of a larger population of promising solutions, which are then used in model building. However, the eda Contents C721model and archive may still become stuck at suboptimal solutions, so to combat this we introduce a decomposition mutation operation which retains most of the attributes of a current solution but attempts large changes in others. A comparison with generic eda, genetic algorithms and the Nelder-Mead method shows that tam-eda is an effective optimization algorithm for a range of test problems.

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Benchmarking nonlinear optimization software in technical computing environments

Pintér

Kampas²

2011

TOP

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Due to copyright restrictions, the access to the full text of this article is only available via subscription.Our strategic objective is to develop a broadly categorized, expandable collection of test problems, to support the benchmarking of nonlinear optimization software packages in integrated technical computing environments (ITCEs). ITCEs—such as Maple, Mathematica, and MATLAB—support concise, modular and scalable model development: their built-in documentation and visualization features can be put to good use also in test model selection and analysis. ITCEs support the flexible inclusion of both new models and general-purpose solver engines for future studies. Within this broad context, in this article we review a collection of global optimization problems coded in Mathematica, and present illustrative and summarized numerical results obtained using the MathOptimizer Professional software package.DRDC-Atlantic ; the National Research Council of Canada ; the University of Ballarat, Australia; Özyegin University ; the TÁMOP, Széchenyi István Universit

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Second derivative Gauss-Newton-based method for solving nonlinear simultaneous equations

Cited by 3 publications

References 1 publication

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell

Neural Network Training By Gradient Descent Algorithms: Application on the Solar Cell

TAM-EDA: Multivariate t Distribution, Archive and Mutation Based Estimation of Distribution Algorithm

Benchmarking nonlinear optimization software in technical computing environments

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