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Generalized equations, variational inequalities and a weak Kantorovich theorem

Authors :
Livinus U. Uko
Ioannis K. Argyros
Source :
Numerical Algorithms. 52:321-333
Publication Year :
2009
Publisher :
Springer Science and Business Media LLC, 2009.

Abstract

We prove a Kantorovich-type theorem on the existence and uniqueness of the solution of a generalized equation of the form $f(u)+g(u)\owns 0$ where f is a Frechet-differentiable function and g is a maximal monotone operator defined on a Hilbert space. The depth and scope of this theorem is such that when we specialize it to nonlinear operator equations, variational inequalities and nonlinear complementarity problems we obtain novel results for these problems as well. Our approach to the solution of a generalized equation is iterative, and the solution is obtained as the limit of the solutions of partially linearized generalized Newton subproblems of the type $Az+g(z)\owns b$ where A is a linear operator.

Details

ISSN :
15729265 and 10171398
Volume :
52
Database :
OpenAIRE
Journal :
Numerical Algorithms
Accession number :
edsair.doi...........8d6112f8720378e3f287042ef200eed6
Full Text :
https://doi.org/10.1007/s11075-009-9275-2