Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set

Abstract

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.