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.
Key words:smooth surface, convex compact set, convex programming problem, projection onto a nonconvex set, necessary conditions for a local minimum, convergence of an algorithm.
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