Abstract
This paper proposes a cumulative function approximation scheme based on Voronoi diagram and an adaptive global optimization method based on its superposability. In the function approximation scheme, the function is approximated as superposition of local quadratic polynomials for the subspaces around respective sample points based on geometric structure that is represented by Voronoi diagram, a technique of computational geometry. This scheme has an ability of cumulative function approximation under its superposability. Based on such a capability, a global optimization method is configured by adaptively arranging new sample points based on tentative optimal solution and the distribution of sample points. Their effectiveness and validity are ascertained through some numerical examples.
