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Robinson’s implicit function theorem. (English) Zbl 1137.49021
Summary: Robinson’s implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.
MSC:
49K27 Optimality conditions for problems in abstract spaces
49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
47H04 Set-valued operators
47J07 Abstract inverse mapping and implicit function theorems involving nonlinear operators
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