A Hybrid Algorithm for Global Optimization Problems

We propose a hybrid algorithm for solving global optimization problems that is based on the coupling of the Simultaneous Perturbation Stochastic Approximation (SPSA) and Newton-Krylov Interior-Point (NKIP) methods 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 NKIP algorithm is applied to the surrogate model subject to bound constraints for obtaining a feasible approximate global solution. We present some numerical results on a set of five small problems and two medium to large-scale applications from reservoir simulations.