DC algorithms in Hilbert spaces and the solution of indefinite infinite-dimensional quadratic programs

This paper considers the DC (Difference-of-Convex-functions) algorithms in a Hilbert space setting and discusses their convergence. Applied to indefinite quadratic programs under linear constraints in Hilbert spaces, among other things, the DCA yields two basic types of iteration algorithms, called the Projection DC decomposition algorithm and the Proximal DC decomposition algorithm . It is proved that, under some mild conditions, any iterative sequence generated by either one of the just mentioned algorithms R -linearly converges to a Karush-Kuhn-Tucker point of the QP problem.