Global optimization with nonfactorable constraints

This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are nonfactorable, defined by a computational model for which no explicit analytical representation is available. A three-phase approach to the global optimization is considered. In the sampling phase, the nonfactorable functions and their gradients are evaluated and an interpolation function is constructed. In the global optimization phase, the interpolants are used as surrogates in a deterministic global optimization algorithm. In the final local optimization phase, the global optimum of the interpolation problem is used as a starting point for a local optimization of the original problem. The interpolants are designed in such a way as to allow valid over- and underestimation functions to be constructed to provide the global optimization algorithm with a guarantee of is an element of-global optimality for the surrogate problem.