A general iterative scheme with applications to convex optimization and related fields

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Abstract
A general iterative scheme including relaxation and a corresponding problem class are presented. Some global convergence results are given. The acceleration of convergence is discussed, The scheme comprises a lot of known iterative methods such as subgradient methods and methods of successive orthogonal projections with relaxation. Applications to convex optimization, convex feasibility problems, systems of convex inequalities, variational inequalities, operator equations and systems of linear equations are given.