Event № 647
Advisor: Prof. Simeon Reich
Abstract: We develop new iterative methods for solving convex feasibility and common fixed point problems, based on the notion of coherence. We also present new concepts and results in Nonlinear Analysis related to the theory of coherence and Opial's demi-closedness principle. We investigate, in particular, the properties of relaxations, convex combinations and compositions of certain kinds of operators defined on a real Hilbert space, under static and dynamic controls, as well as other properties regarding the algorithmic structure of some operators. Our iterative techniques are applied, for example, to the study of various metric and subgradient projection methods. Furthermore, all the methods are presented in both weak and strong convergence versions.