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

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.

Keywords:

• Hilbert space
• iterative methods
• relaxation parameters
• nonexpansive operators
• convex optimization
• convex feasibility problem
• subgradient methods
• successive projections

AMS Subject Classification:

• Primary:65 K 10
• Primary:49 D 20
• Secondary:49 D 45