Sentence examples for using a nonlinear optimization from inspiring English sources

Maximization is achieved using a nonlinear optimization technique, where the optimal multiplication factors as a function of the hyper-parameters are found as α p ( f ) = − | b | − ( | b | 2 − 4 ac ) 1 / 2 2 a b | b | (31).

where J α p ( f ) = α p I 2 ( f ) is the Jacobian of the scaling transform and Ψ p (f) is the inverse scale matrix in (15) which depends on p. Maximization with respect to m can be achieved using a nonlinear optimization technique [34], where the optimal scaling factors for a given m are given by α p ( f ) = tr ( Ψ p ( f ) R p − 1 ( f ) ) Im. (17).

The solutions for both formulations are obtained by using a nonlinear optimization software.

The modeling parameters have been extracted using a nonlinear optimization algorithm.

Then, design optimization for accuracy has been performed by using a nonlinear optimization technique.

The initial projection matrix is then refined by minimizing the distance from the original and reprojected head points by using a nonlinear optimization algorithm.

The hybrid tracker uses a nonlinear optimization framework to incorporate both feature correspondence and brightness constraints, and achieves reliable 3D face tracking in real-time.

In this article, we used a nonlinear optimization routine by Newton-Raphson ridge method in SAS IML (SAS Institute Inc., Cary, NC).

VB-ECD is a point-source inversion method that uses a nonlinear optimization algorithm to fit a number of dipoles simultaneously, with different prior distributions on their locations and moments, to all of the sensor data (i.e., with no a priori selection of channels).

Then, using a nonlinear design optimization code, the partial admission of an impulse supersonic turbine is optimized.

Based on measured normal operating data from an industrial stainless steel plant, parameter identification is basically carried out using a nonlinear least-squares optimization algorithm for the whole annealing furnace, to estimate optimal values of uncertain parameters, such as emissivities.