A general iterative method for hierarchical variational inequality problems in Hilbert spaces and applications

Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H . Let F be a maximal monotone operator on H such that the domain of F is included in C . Let 0...

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Vydané v:	Positivity Ročník 16; číslo 3; s. 429 - 453
Hlavní autori:	Lin, Lai-Jiu, Takahashi, Wataru
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel Springer Science and Business Media LLC 01.09.2012 SP Birkhäuser Verlag Basel Springer Springer Nature B.V
Predmet:	Calculus of variations and optimal control Calculus of Variations and Optimal Control; Optimization Econometrics Equilibrium Exact sciences and technology Fourier Analysis Hilbert space Inequality Iterative methods Mapping Mathematical analysis Mathematics Mathematics and Statistics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Operator Theory Partial differential equations Potential Theory Sciences and techniques of general use Studies Variance analysis Asia 58E35 47H10 Resolvent Equilibrium problem Inverse-strongly monotone mapping Strict pseudo-contraction Maximal monotone operator Iteration procedure 47H05 Fixed point Hierarchical variational inequality problems Space application Solution uniqueness Strong convergence Variational methods Nonlinear analysis Iterative method Mapping Monotone operator Contraction Mathematical analysis Variational inequality Hilbert problem Hilbert space Inverse
ISSN:	1385-1292, 1572-9281
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Abstract	Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H . Let F be a maximal monotone operator on H such that the domain of F is included in C . Let 0 < k < 1 and let g be a k -contraction of H into itself. Let V be a -strongly monotone and L -Lipschitzian continuous operator with and L > 0. Take as follows: In this paper, under the assumption , we prove a strong convergence theorem for finding a point which is a unique solution of the hierarchical variational inequality Using this result, we obtain new and well-known strong convergence theorems in a Hilbert space which are useful in nonlinear analysis and optimization.
AbstractList	Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H . Let F be a maximal monotone operator on H such that the domain of F is included in C . Let 0 < k < 1 and let g be a k -contraction of H into itself. Let V be a -strongly monotone and L -Lipschitzian continuous operator with and L > 0. Take as follows: In this paper, under the assumption , we prove a strong convergence theorem for finding a point which is a unique solution of the hierarchical variational inequality Using this result, we obtain new and well-known strong convergence theorems in a Hilbert space which are useful in nonlinear analysis and optimization. Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let > 0 and let A be an -inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H. Let F be a maximal monotone operator on H such that the domain of F is included in C. Let 0 < k < 1 and let g be a k-contraction of H into itself. Let V be a -strongly monotone and L-Lipschitzian continuous operator with > 0 and L > 0. Take R as follows: In this paper, under the assumption (A + B)10 F10 = , we prove a strong convergence theorem for nding a point z0 (A + B)10 F10 which is a unique solution of the hierarchical variational inequality (Vg)z0, q z0 0, q (A + B)10 F10. Using this result, we obtain new and well-known strong convergence theorems in a Hilbert space which are useful in nonlinear analysis and optimization. [PUBLICATION ABSTRACT]
Author	Wataru Takahashi Lai-Jiu Lin
Author_xml	– sequence: 1 givenname: Lai-Jiu surname: Lin fullname: Lin, Lai-Jiu email: maljlin@cc.ncue.edu.tw organization: Department of Mathematics, National Changhua University of Education – sequence: 2 givenname: Wataru surname: Takahashi fullname: Takahashi, Wataru organization: Department of Mathematics, National Changhua University of Education, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology
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Cites_doi	10.1016/j.na.2006.08.032 10.1023/A:1023073621589 10.1007/BF01190119 10.1007/s10957-010-9713-2 10.1016/j.jmaa.2006.06.055 10.1016/j.na.2009.03.060 10.1090/S0002-9904-1967-11864-0 10.1016/j.na.2008.02.042 10.1016/0022-247X(67)90085-6 10.1006/jmaa.1999.6615 10.1017/S0004972700020116 10.1023/A:1025407607560 10.1016/j.na.2010.03.058 10.1137/050624315 10.1016/j.na.2007.05.032 10.1007/BF01109805 10.1016/j.jmaa.2005.05.028 10.2140/pjm.1970.33.209
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Keywords	58E35 47H10 Resolvent Equilibrium problem Inverse-strongly monotone mapping Strict pseudo-contraction Maximal monotone operator Iteration procedure 47H05 Fixed point Hierarchical variational inequality problems Space application Solution uniqueness Strong convergence Variational methods Nonlinear analysis Iterative method Mapping Monotone operator Contraction Mathematical analysis Variational inequality Hilbert problem Hilbert space Inverse
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Snippet	Let H be a real Hilbert space and let C be a nonempty closed convex subset of H . Let α > 0 and let A be an α -inverse-strongly monotone mapping of C into H... Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let > 0 and let A be an -inverse-strongly monotone mapping of C into H and let...
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SubjectTerms	Calculus of variations and optimal control Calculus of Variations and Optimal Control; Optimization Econometrics Equilibrium Exact sciences and technology Fourier Analysis Hilbert space Inequality Iterative methods Mapping Mathematical analysis Mathematics Mathematics and Statistics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Operator Theory Partial differential equations Potential Theory Sciences and techniques of general use Studies Variance analysis
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Title	A general iterative method for hierarchical variational inequality problems in Hilbert spaces and applications
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