Generalized equations, variational inequalities and a weak Kantorovich theorem

DOI10.1007/s11075-009-9275-2zbMath1179.65063OpenAlexW2046838281MaRDI QIDQ1039274

Ioannis K. Argyros, Livinus Ugochukwu Uko

Publication date: 27 November 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9275-2

zbMATH Keywords

variational inequalityHilbert spacemaximal monotone operatornonlinear complementarity problemnonlinear operator equationgeneralized equationKantorovich theorem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Variational inequalities (49J40) Newton-type methods (49M15) Set-valued and variational analysis (49J53) Iterative procedures involving nonlinear operators (47J25) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for variational inequalities and related problems (65K15)

Related Items (4)

Local convergence of Newton’s method for solving generalized equations with monotone operator ⋮ A generalized extragradient method for variational inequalities of the second kind ⋮ Kantorovich's theorem on Newton's method for solving generalized equations under the majorant condition ⋮ Expanding the applicability of the Kantorovich's theorem for solving generalized equations using Newton's method

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• On the monotonicity of the gradient of a convex function
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• Optimal Error Bounds for the Newton–Kantorovich Theorem
• Extensions of Kantorovich theorem to complementarity problem
• On the Kantorovich Hypothesis for Newton’s Method

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