The UTEP group is developing a hybrid algorithm for solving global optimization problems that is based on the coupling of a stochastic global method (Simultaneous Perturbation Stochastic Approximation, Simulated Annealing, Genetic Algorithms) and a local method (Newton-Krylov Interior-Point) via a surrogate model. There exist verified algorithms for finding approximate global solutions, but our technique will further guarantee that such solutions satisfy physical bounds of the problem. First, the SPSA algorithm conjectures regions where a global solution may exist. Next, some data points from the regions are selected to generate a continuously differentiable surrogate model that approximates the original function. Finally, the interior point Newton algorithm is applied to the surrogate model subject to bound constraints for obtaining a feasible approximate global solution. Numerical results in small to medium-scale problems are presented.