Optimization Toolbox Release Notes 
New Features
This section summarizes the new features and enhancements introduced in the Optimization Toolbox 2.2.
If you are upgrading from a release earlier than Release 12.1, then you should also see New Features of the Optimization Toolbox 2.1.1 Release Notes.
New fsolve Default Algorithm
The fsolve
function, which is used to solve systems of nonlinear equations, has a new default algorithm for mediumscale systems where the number of equations is equal to the number of variables. The new algorithm uses a trustregion dogleg method that has improved convergence properties over the previous default method. It is based on the algorithm described in [1].
MediumScale Is Now the Default Method
In keeping with the new default trustregion dogleg algorithm, fsolve
now defaults to the mediumscale method. The default for the 'LargeScale'
parameter is changed to 'off'
.
To use the largescale fsolve
method, which was the default in Versions 2.0 and 2.1, specify the largescale method using code similar to
New 'NonlEqnAlgorithm' Parameter
A new 'NonlEqnAlgorithm' fsolve
parameter enables you to choose the LevenbergMarquardt or GaussNewton algorithm over the trustregion dogleg algorithm. 'NonlEqnAlgorithm' has three options: 'dogleg'
(default), 'lm'
(LevenburgMarquart), and 'gn'
(GaussNewton). Specify the use of an algorithm other than the default with code similar to
See Upgrading from an Earlier Release for more information.
References
[1] J.J. Moré, B.S. Garbow, and K.E. Hillstrom, "User Guide for MINPACK  1," Argonne National Laboratory, Rept. ANL8074, 1980
Function Summary
Version 2.2 of the Optimization Toolbox provides the following functions with new or changed capabilities.
Optimization Functions with New or Changed Capabilities
Function 
Enhancement or Change 

The trustregion dogleg algorithm is now the default for mediumscale systems of equations where the number of equations is equal to the number of variables. See New fsolve Default Algorithm for more information. 

A new 'NonlEqnAlgorithm' parameter, which applies only to fsolve , enables you to choose the LevenbergMarquardt or GaussNewton algorithm over the new default trustregion dogleg algorithm. 
Optimization Toolbox Release Notes  Major Bug Fixes 