An Implicit Extragradient Method for Hierarchical Variational Inequalities
Copyright policy )An Implicit Extragradient Method for Hierarchical Variational Inequalities
AbstractAs a well-known numerical method, the extragradient method solves numerically the variational inequality "Equation missing" of finding "Equation missing" such that "Equation missing", for all "Equation missing". In this paper, we devote to solve the following hierarchical variational inequality "Equation missing" Find "Equation missing" such that "Equation missing", for all "Equation missing". We first suggest and analyze an implicit extragradient method for solving the hierarchical variational inequality "Equation missing". It is shown that the net defined by the suggested implicit extragradient method converges strongly to the unique solution of "Equation missing" in Hilbert spaces. As a special case, we obtain the minimum norm solution of the variational inequality "Equation missing".
- Cheng Shiu University Taiwan
- Tianjin Polytechnic University China (People's Republic of)
T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Variational inequalities, hierarchical variational inequalities, implicit extragradient method, strong convergence, Iterative procedures involving nonlinear operators, Other numerical methods in calculus of variations, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Geometry and Topology, Analysis
T57-57.97, QA299.6-433, Applied mathematics. Quantitative methods, Applied Mathematics, Variational inequalities, hierarchical variational inequalities, implicit extragradient method, strong convergence, Iterative procedures involving nonlinear operators, Other numerical methods in calculus of variations, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Geometry and Topology, Analysis
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