This paper presents an algorithm for finding global solutions of nonconvex nonlinear programs (NLPs) and mixed-integer nonlinear programs (MINLPs). The approach is based on the solution of a sequence of convex underestimating subproblems generated by evolutionary subdivision of the search region. The key components of the algorithm are new optimality-based and feasibility-based range reduction tests. The former use known feasible solutions and perturbation results to exclude inferior parts of the search region from consideration, while the latter analyze constraints to obtain valid inequalities. Furthermore, the algorithm integrates these devices with an efficient local search heuristic. Computational results demonstrate that the algorithm compares very favorably to several other current approaches when applied to a large collection of global optimization and process design problems. It is typically faster, requires less storage and it produces more accurate results.