Schott
Iterative Solution of Convex Problems by Fejer-monotone Methods
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

65J15 Equations with nonlinear operators (do not use 65Hxx)

Abstract: Let $H$ be a Hilbert space and $M$ be an implicitely given nonempty,
convex and closed subset (solution set of a convex problem). Besides
let $Q\supseteq M$ be a further convex and closed subset (feasible
domain, constraints). We consider iterative methods
\[x_{k+1} \in g_k(x_k), x_0 \in Q \]
with point-to-set mappings $g_k:Q \rightarrow {\Bbb P} (Q)$, wich are
Fejer-monotone relative to $M$ (or $M$-Fejer-monotone). We present
conditions ensuring strong convergence of $(x_k)$ to a fixed element
$x^*$ in $M$. Finally we give applications of the results to various
types of convex.

Keywords: Convex problems, Fejer-momotone mappings, Fejer-kernels, Iterative methods of Fejer-type