We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the objective, which is then used within a trust-region framework...
Regarding the minimization method for the objective function, the ENN and the BNN are different. The ENN is based on the Gauss–Newton method using the calculation of the Hessian matrix. However, the BNN relies on the gradient descent method based on error backpropagation. Specifically, both the...
Derivative Free Conjugate Gradient Method via Broyden’s Update for solving symmetric systems of nonlinear equations. J. Phy. Conf. Ser. 2019, 1366, 012099. [Google Scholar] [CrossRef] Zhou, W. A modified BFGS type quasi-Newton method with line search for symmetric nonlinear equations problems...
Zhang, H.C., Conn, A.R., Scheinberg, K.: A derivative-free algorithm for the least-squares minimization. SIAM J. Optim. 20, 3555–3576 (2010)CrossRefMathSciNetMATH About this Article Title Local analysis of a spectral correction for the Gauss-Newton model applied to quadratic residual ...
In the case of completely developed unidirectional flows, the normal component of the surface traction at a cross section perpendicular to the flow field is identical to the pressure field, since the normal derivative of the normal velocity at such a cross section is zero, with the tangential ...
To circumvent this difficulty, a derivative-free global optimization algorithm was developed by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. They further checked the convergence of the proposed method. 3.5. Parallel Implementation Parallel ...
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This method improves element qualities by maximizing the minimum area of an element and solves the problem using linear programming. However, this method requires the mesh quality to be convex. Also, other derivative free mesh optimization algorithms need many initial parameters to be chosen or are...
23) were estimated by the Gauss–Newton method modified by the SAS NLIN procedure (SAS University Edition, Sas Institute Inc. Cary, CA, USA24). The maximum number of interactions used was 100 (one hundred). The criterion used to evaluate the model was the coefficient of determination (R2)...
Derivative-free search method: Derivative-free algorithms have the capability to minimize the error of an objective function between measurements and prediction in a multi-dimensional problem. The approach is based on an iterative scheme where each trial solution is compared with the best previous one...