Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces
In the present paper, we study the finite termination of sequences generated by inexact proximal point algorithms for finding zeroes of a maximal monotone (set-valued) operator \(T\) on a Hilbert space. Under some mild conditions, we get that a sequence generated by inexact proximal point algorithm stops after a finite number of iterations. Our results extend the corresponding results in Rockafellar (SIAM J Control Optim 14:877898, 1976). In particular, for optimization problems, our results improve corresponding results in Ferris (Math Progr 50:359366, 1991). As applications, we obtain finite termination of projected gradient method.
finite termination inexact proximal point algorithms maximal monotone projected gradient method 49j53 47h04 65k10