A new sampling strategy is presented for kriging-based global modeling. The strategy is used within a kriging/response surface (RSM) algorithm for solving NLP containing black-box models. Black-box models describe systems lacking the closed-form equations necessary for conventional gradient-based optimization. System optima can be alternatively found by building iteratively updated kriging models, and then refining local solutions using RSM. The application of the new sampling strategy results in accurate global model generation at lower sampling expense relative to a strategy using randomized and heuristic-based sampling for initial and subsequent model construction, respectively. The new strategy relies on construction of an initial kriging model built using sampling data obtained at the feasible region's convex polytope vertices and centroid. Updated models are constructed using additional sampling information obtained at Delaunay triangulation centroids. The new sampling algorithm is applied within the kriging-RSM framework to several numerical examples and case studies to demonstrate proof of concept. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 220-240, 2010