Abstract:
A numerical algorithm is proposed for minimizing a convex function on the set-theoretic difference between a set of points of a smooth surface and the union of finitely many convex open sets in $n$-dimensional Euclidean space. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
Key words:smooth surface, open convex set, convex programming problem, necessary conditions for a local minimum, convergence of an algorithm.
