The six variables for m 1,m 2,d 1,d 2,v 1,v 2 were found by a nonlinear constrained optimization with the variances constrained to lie above the minimum values corresponding to the choices for m,d in each period as is consistent with the frontier for the period.
Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass.
In OK, the weighing coefficient λ i can be calculated by solving an optimization problem, whereby, the variance of errors will be minimized, subjected to unbiased condition.
We solve the dual [ 44] of the variance optimization problem mentioned above.
The classes used in the maps have been calculated applying the Jenks natural breaks optimization algorithm, which reduces the variance within classes and maximizes the variance between classes [ 17].
In the optimization process variance functions and cost functions have to be linked in order to derive the optimal (i.e. most cost-efficient) sampling alternative.
The best reference trajectory is found by solving an additional optimization problem whose criterion penalizes the variance of the control signal.
The variance weighed optimization procedure developed by van der Heijden et al. (1994) was used to test elemental recovery and subsequently to reconcile the measured primary fermentation data, based on elemental balancing; it was also used to calculate the biomass-specific uptake and production rates.
Another quite realistic approach is to consider the optimization as a multiple objective optimization problem where the cost and the variance are simultaneously minimized functions.
The optimization of the noise variance, σ d 2, as an hyperparameter during the training process led to a value of 0.27 log units, similar to the values of about 0.3 log units reported by Prusis et al.[61] in a recent study with similar experimental setup.
