What Is Optimization Toolbox?

3 Standard AlgorithmsCase 3.Case 4.whereCases 1 and 2 show the procedures performed when the valueis positive. Cases 3 and 4 show the procedures performed when the valueis negative. The notationvalue of the set .refers to the smallestAt each iteration a cubicly interpolatedsteplength is calculated andthen used to adjust the step length parameter . Occasionally, for verynonlinear functions can be negative, in which case is given a value of .Certain robustness measures have also been included so that, even in the casewhen false gradient information is supplied, you can achieve a reduction in f(x)by taking a negative step. You do this by setting when fallsbelow a certain threshold value (e.g., 1e-8). This is important when extremelyhigh precision is required, if only finite difference gradients are available.3-14