The authors propose an algorithm for solving the problem min f(x), s.t.
, with X a closed convex subset of the Hilbert space H and f:H
smooth function of the form
and P denotes the projection on X. The norms
corresponding to the projection on X and the differentiation operators are generally different, depending on the structure of X and the Hessian of f at
, respectively. Under some additional assumptions the algorithm attains a superlinear rate of convergence.