Interval arithmetic algorithms A.l and A.2 that determine computationally rigorous bounds on the global minimizers of continuous functionswithout inequality constraints and with inequality constraintsrespectively are described. It is assumed that, for A.land that forand. Computational experience indicates that A.l and A.2 always succeed, although in some cases more than one interval containing a global minimizer is found. Numerical results obtained from Sun Pascal implementations of A.l and A.2 are presented.