Uniform convergence for multi-valued algorithms (Q1386799)

In a Banach space setting abstract algorithms are studied for finding a fixed point of the multivalued one-parametric generating operator with weakly compact values. To this end abstract algorithms with disturbances are considered while the disturbances of the algorithm are possibly considered as a control of the iterative process or as an error of the approximate calculations. Known sufficient conditions for the convergence and keeping the convergence rate of undisturbed algorithms with single-valued generating operator are generalized for those with disturbed multivalued generating operator and a comparative study of a set of sufficient conditions are carried out. These theoretical results as applied to unconstrained nonlinear optimization problems are presented.