Dealing with stochastic optimization
In difference to deterministic optimization, by using stochastic optimization one can find a different solution with the same starting values. This should also allow us to trap not (always) to a local optima.
Simplified procedures (Star Trek, Spaceballs, and Spaceballs princess)
As mentioned in the introduction of this chapter, in principle a (fine) grid, which should cover the whole distribution of f, can be used and evaluated for each grid point (Star Trek). Those grid coordinates having a maximum/minimum, provide an approximate solution of the optimization problem. Grid-based deterministic solutions to other problems are, for example, the Stahel-Donoho estimator for outlier detection (Stahel 1981a) (Stahel 1981b) or the raster-based search for principal components of a data set using grid-based projection pursuit methods (Croux, Filzmoser, and Oliveira 2007).
To move from this deterministic approach to an approach which includes randomness, one can just...
