An algorithm for continuous type optimal spherical facility location problem (Q2721874)

The paper is devoted to continuous facility location problem on a sphere, where only one facility should be placed to minimize an average weighted spherical distance between the facility and points from smooth curved surface on the sphere. The weight is described by positive continuous function defined on the surface. The problem was obtained by a generalization of the planar Euclidean continuous facility location problem. The authors explored properties of the problem and proved that its objective function is strictly spherical convex and that it is differentiable. They also derived optimality condition. Making use of the revealed properties, they suggested an algorithm based on gradient method and proved that the algorithm either stops at the optimal solution after finite number of steps, or it generates infinitive sequence of points, which converges to the optimal solution.