Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities



Assume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We construct an iterative algorithm with variable parameters which generates a sequence {x n } from an arbitrary initial point x 0H. The sequence {x n } is shown to converge in norm to the unique solution u of the variational inequality \(\langle F(u^{\ast}), v - u^{\ast}\rangle \geq 0, \quad \forall v \in C.\)

Key Words

Iterative algorithms modified hybrid steepest-descent methods with variable parameters convergence nonexpansive mappings Hilbert spaces 


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© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan
  3. 3.Department of Applied MathematicsNational Sun Yat-Scn UniversityKaohsiungTaiwan

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