A quasi-Monte Carlo method for the approximate computation of the extreme values of a function

The applicability of Monte Carlo methods to a wide range of problems in numerical analysis is well known. If one replaces the random sampling procedure, on which a Monte Carlo method is based, by a deterministic selection scheme appropriate to the problem at hand, one arrives at techniques that are collectively called “quasi-Monte Carlo methods”. These methods have the advantage that one can usually establish effective a priori error bounds for them which are often better than the probabilistic Monte Carlo bounds. Very successful implementations of such methods have been developed for the purposes of numerical integration and approximate solution of integral equations. We refer to [5] for a survey of quasi-Monte Carlo methods.