Infinitely constrained (or semi-infinite) optimization can be successfully used to solve a significant variety of optimization-based engineering design problems. In this paper a new algorithm for the numerical global solution of nonlinear and nonconvex, infinitely constrained problems is proposed. At the upper level this hybrid algorithm is a partially elitist genetic algorithm that uses, at the lower level, an interval procedure to compute a penalty-based fitness function. The deterministic nature of the interval procedure, whose global convergence with certainty is established by using concepts of interval analysis, guarantees the feasibility of the estimated global solution provided by the hybrid algorithm. Computational results are reported for three test problems and the hybrid algorithm is applied to the optimal worst-case H-2 design of a proportional-integral-derivative (PID) controller for an uncertain nonminimum-phase plant.