A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces (1999)
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BibTeX
@MISC{Bauschke99aweak-to-strong,
author = {Heinz H. Bauschke and Patrick L. Combettes},
title = {A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces},
year = {1999}
}
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Abstract
We consider a wide class of iterative methods arising in numerical mathematics and optimization which are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods which makes them strongly convergent without additional assumptions. Several applications are discussed. AMS 1991 subject classification. Primary: 65J15, 47N10; secondary 41A29, 47H05, 47H09, 65K10, 90C25. Key words. Convex feasibility, Fej'er-monotonicity, firmly nonexpansive mapping, fixed point, Haugazeau, maximal monotone operator, projection, proximal point algorithm, resolvent, subgradient algorithm. 1 Introduction Let H be a real Hilbert space with scalar product h\Delta j \Deltai, norm k \Delta k, and distance d. In 1965, Bregman [5] proposed a simple iterative method for finding a common point of m intersecting closed convex sets (S i ) 1im in H. He showed that, given an arbitrary starting point x 0 2 H, the sequence (x n ) n0 gene...
