Nonlinear least squares regression of Antoine vapor pressure coefficients using analytical derivatives and a Gauss Newton algorithm

by Trent Guidry 1. January 2012 09:49
The Antoine correlation is a simple equation that can be used to model the saturated liquid vapor pressure of a pure chemical substance. The analytical derivatives of the Antoine correlation along with a Gauss Newton algorithm can be used for the nonlinear least square regression of the correlation parameters.

Nonlinear Optimization Using a Broyden Fletcher Goldfarb Shanno (BFGS) Algorithm

by Trent Guidry 31. December 2011 10:24
The Broyden Fletcher Goldfarb Shanno (BFGS) algorithm is a popular quasi Newton algorithm. The quasi Newton algorithms are based on Newton's method for optimization and use an approximation of the Hessian matrix based on past positions and functional values rather than an analytically or numerically calculated one.

Nonlinear Optimization using the Davidon Fletcher Powell (DFP) Algorithm

by Trent Guidry 30. December 2011 12:25
The Davidon Fletcher Powell (DFP) algorithm was the first quasi Newton algorithm created. The quasi Newton algorithms are based on Newton's method for optimization and use an approximation of the Hessian matrix based on past positions and functional values rather than an analytically or numerically calculated one.

Nonlinear Optimization using Newton’s Method

by Trent Guidry 27. December 2011 13:28
Newton's method for optimization is similar to Newton's method for root finding. The primary difference between the two is that instead of finding zero values for the system of equations it finds zero values for the system of first derivatives of the equations.

Nonlinear least squares regression of multiple weighted simultaneous equations using a general purpose optimization routine

by Trent Guidry 11. December 2011 09:39
General purpose optimization routines, such as the Simplex, the conjugate gradient, a quasi Newton, etc., can be used for the nonlinear least squares regression of parameters for systems of simultaneous equations.

Implementing a Levenberg Marquardt algorithm for the nonlinear least squares regression of multiple weighted simultaneous equations in C#

by Trent Guidry 10. December 2011 12:04
In this post I create a Levenberg Marquardt class in C# that can be used for the nonlinear least squares regression of multiple simultaneous weighted equations.

Implementing a Levenberg algorithm for the nonlinear least squares regression of multiple weighted simultaneous equations in C#

by Trent Guidry 10. December 2011 11:03
In this post I create a Levenberg class in C# that can be used for the nonlinear least squares regression of multiple simultaneous weighted equations.

Implementing a Gauss Newton algorithm for the nonlinear least squares regression of multiple weighted simultaneous equations in C#

by Trent Guidry 10. December 2011 09:20
In this post I create a Gauss Newton class in C# that can be used for the nonlinear least squares regression of multiple simultaneous weighted equations.