Bayesian Methods
                P-Algorithms

The Bayesian approach to global optimization aims at producing methods that despite having a rather poor efficiency in worst case analysis can be used to solve average case problems efficiently.

After a sample point has been evaluated a stochastic model of the problem function based on all sample points is computed.

Then a utility function reflecting the rewards of continuing sampling in a particular region is maximized in order to find the "best" candidate for a new sample point.

The purpose of the utility function is to find trade-off between sampling in known promising regions versus sampling in under-explored regions or regions where the variation in function values is high. [Kushner 1962].

Due to the large overhead in selecting sample points these methods are only suited for problems where the function is very expensive to evaluate.

There are many papers by Mockus and Zilinskas in this area [Törn and Zilinskas 1978].