Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set
Abstract:
The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.
Key words:spherical surface, convex closed set, gradient projection method, Newton's method, necessary conditions for a local minimum, convergence of an algorithm.
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