Numerical Algorithm for Minimizing a Convex Function on the Intersection of a Smooth Surface and a Convex Compact Set

Abstract

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a smooth surface and a convex compact set in finite-dimensional Euclidean space is proposed. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are studied, and the convergence of the algorithm is analyzed.