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Mathematical programming includes the study of the mathematical structure of optimization problems, the invention of methods for solving these problems, the study of the mathematical properties of these methods, and the implementation of these methods on computers.
We used the WEKA implementation of these methods [49].
However, for a particular trial, the implementation of these methods requires extensive computer programming.
Computational implementation of these methods, recent improvements to the computer code, and parallelization strategies are described in detail.
The chapter describes three nontest methods and the work necessary for the coordination of the implementation of these methods.
Numerical results from our implementation of these methods are shown to illustrate connections between the physical measurements and spatial characteristics of the optimized knot configurations.
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The next section recalls some basic mathematical concepts of the continuation approaches, with a focus on the numerical implementations of these methods.
Since 2001 the implementations of these methods are carried out according to different requirements for tramway vehicles, metro vehicles, and main line EMU vehicles etc.
However, there are noticeable shortcomings in implementations of these methods especially the use of arbitrary function as a starting value, an in-appropriate choice of starting function may affect the rate of convergence, see [11, 12].
Finally, a further assumption for unbiased treatment effect estimates in parametric implementations of these methods is that the model reflects the true relationship between the outcome of interest and the covariates used for the adjustment [17].
Moreover, although new data analysis methods are also appearing, the individual implementations of these methods may only be available on specific platforms and must be accessed according to differing protocols.
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