defaultCA: Default settings for online whitening functionality
In SACOBRA: Self-Adjusting COBRA

Description Usage Details Value See Also

Sets default values for the online whitening functionality in order to handle function with high conditioning. With the call setOpts(cobra$CA,defaultCA()) it is possible to extend a partial list cobra$CA to a list containing all CA-elements (the missing ones are taken from defaultCA()).

As RBF interpolations face severe difficulties to deliver reasonable models for functions with high conditioning, we try to transform the function with high conditioning f(\vec{x}) to a better conditioned one g(\vec{x}) which is easier to model.

g(\vec{x})=f(\mathbf{M}(\vec{x}-\vec{x}_c))

A possible transformation matrix M is the squared inverse of the Hessian matrix \mathbf{H}^{-0.5}, assuming that M is chosen with the following assumption:

\frac{\partial^2 g(\vec{x})}{\partial \vec{x}^2}=\mathbf{I}

1	defaultCA()

The current version is only relevant for unconstrained problems. It this stage it is not recommended to apply the online whitening to expensive optimization problems As it demands large number of function evaluations. Every online whitening call demands 4d^2+4d function evaluations.

CA, a list of the follwing elements:

`active`	Set to TRUE if an online whitening of the fitness function is desired
`HessianType`	["real"] You can choose if the Hessian amtrix is evaluted on the real function or on the surrogate model ["real", "surrogate"]. Please note that the determination of Hessian matrix on the real function at each point costs 4*d^2+d real function evalautions
`ITERS`	[seq(10,500,10)], pass a vector of integers to this paramter then the Hessian matrix will be updated only in the given iterations, we recommended applying the online-whitening each 10 iterations after the `10d` initial iterations. `seq(10d,maxIter,10)`, where `d` is the dimensionality of the optimization problem . If set as the charachter "all" then the Hessian matrix will be updated in each iteration and whitening procedure will be repeated
`alpha`	[1] you can assign any real value to this parameter. Only values between 0 to 2 are suggested. This value is used in order to modify the transformation center `tCenter` as follows: xbest+alpha*(grad), and grad is the direction of the last improvment