A new method for minimax location on a sphere

The problem of finding a minimax facility location point on a sphere is formulated as a mathematical programming problem with a linear objective function and all-but-one linear constraints in four variables for both hemispherical and nonhemispherical demand points using elementary optimization principles. For the hemispherical case the model is shown to be a convex programming problem, and for the nonhemispheric case the model is shown to be a nonconvex programming problem. In the former case the local solution is global, and in the latter case a strategy to determine the global minimax point is presented. An advantage of the proposed formulation, unlike existing methods, is that there is no need to develop a special purpose algorithm to optimize the models. Instead, any nonlinear optimization software can be used to solve the problem.