The Adaptive Projected Subgradient Method over the Fixed Point Set of Strongly Attracting Nonexpansive Mappings
Konstantinos Slavakis, Isao Yamada, Nobuhiko Ogura · Numerical Functional Analysis and Optimization · 2006
This paper presents an algorithmic solution, the adaptive projected subgradient method, to the problem of asymptotically minimizing a certain sequence of non-negative continuous convex functions over the fixed point set of a strongly attracting nonexpansive mapping in a real Hilbert space. The method generalizes Polyak's subgradient algorithm for the convexly constrained minimization of a fixed nonsmooth function. By generating a strongly convergent and asymptotically optimal point sequence, the proposed method not only offers unifying principles for many projection-based adaptive filtering algorithms but also enhances the adaptive filtering methods with the set theoretic estimation's armory by allowing a variety of a priori information on the estimandum in the form, for example, of multiple intersecting closed convex sets.