Abstract
Taking advantage of recent developments in the theory of generalized differentiation of multifunctions, we present in a unified manner a general iterative procedure for solving generalized equations. This procedure is based on a certain type of approximation of functions called point-based approximation together with a linearization of the multifunctions. Our theorem encompasses the Newton method and extends in the same time, many methods of resolution of generalized equations that have been developed during the last two decades.
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Acknowledgements
The authors are grateful to the anonymous referees and editor for all the suggestions and comments that allowed us to improve the quality of the paper. Research of the first author was partially supported by Contract EA4540 (France). Research of the second author was partially supported by CNPq Grants 434796/2018-2.
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Communicated by Asen L. Dontchev.
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Gaydu, M., Silva, G.N. A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction. J Optim Theory Appl 185, 207–222 (2020). https://doi.org/10.1007/s10957-020-01635-8
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DOI: https://doi.org/10.1007/s10957-020-01635-8
Keywords
- Generalized equation
- Generalized point-based approximations
- Differentiable multifunction
- Newton method
- Metric regularity