An algorithm is proposed for the global solution of generalized semi-infinite programs (GSIPs) without convexity assumptions. It is an extension of the algorithm in [A. Mitsos. Global optimization of semi-infinite programs via restriction of the right hand side. Optimization, 60(10-11):1291--1308, 2011] which in turn can be seen as a feasible-point adaptation of [J.~W. Blankenship and J.~E. Falk. Infinitely constrained optimization problems. Journal of Optimization Theory and Applications, 19(2):261--281, 1976.]. Under mild assumptions compared to alternative algorithms, the algorithm terminates finitely with a guaranteed feasible point, and a certificate of $\varepsilon^f$-optimality. It is based on solving a series of regular nonlinear programs (NLP), thus shifting the nonconvexity to the global NLP solver. The main idea of generating feasible points is a restriction of the constraints right-hand-side by progressively smaller $\varepsilon^g>0$ and a successively finer discretization of the parameter set. The theoretical properties are discussed and numerical results are given.