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2010•Taiwanese Journal of MathematicsOpen access

VISCOSITY METHOD FOR HIERARCHICAL FIXED POINT APPROACH TO VARIATIONAL INEQUALITIES

Hong‐Kun Xu

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Abstract

A viscosity method for a hierarchical fixed point approach to variational inequality problems is presented. This method is used to solve variational inequalities where the involving operators are complements of nonexpansive mappigs and the solutions are sought in the set of the fixed points of another nonexpansive mapping. Such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings.

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A viscosity method for a hierarchical fixed point approach to variational inequality problems is presented. This method is used to solve variational inequalities where the involving operators are complements of nonexpansive mappigs and the solutions are sought in the set of the fixed points of another nonexpansive mapping. Such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings.

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Available abstract

A viscosity method for a hierarchical fixed point approach to variational inequality problems is presented. This method is used to solve variational inequalities where the involving operators are complements of nonexpansive mappigs and the solutions are sought in the set of the fixed points of another nonexpansive mapping. Such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings.

Key concepts: Variational inequality, Mathematics, Fixed point, Monotone polygon, Viscosity, Regular polygon, Applied mathematics, Viscosity solution

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