Convex programming in Hilbert space

This note gives a construction for minimizing certain twice-differentiable functions on a closed convex subset C, of a Hubert Space, H. The algorithm assumes one can constructively "project" points onto convex sets. A related algorithm may be found in Cheney-Goldstein l, where a constructive fixed-point theorem is employed to construct points inducing a minimum distance between two convex sets. In certain instances when such projections are not too difficult to construct, say on spheres, linear varieties, and orthants, the method can be effective. For applications to control theory, for example, see Balakrishnan 2, and Goldstein