Geodesic
Metric regularity properties of monotone mappings
Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 1-8.

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The theory of metric regularity deals with properties of set-valued mappings that provide estimates useful in solving inverse problems and generalized equations. Maximal monotone mappings, which dominate applications related to convex optimization, have valuable special features in this respect that have not previously been recorded. Here it is shown that the property of strong metric subregularity is generic in an almost everywhere sense. Metric regularity not only coincides with strong metric regularity but also implies local single-valuedness of the inverse, rather than just of a graphical localization of the inverse. Consequences are given for the solution mapping associated with a monotone generalized equation.
Keywords: maximal monotone mappings, metric regularity, generic subregularity, generalized equations, inverse problems, variational inequalities, convex optimization, 90C31, 49K40, 90C25 
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Rockafellar, Ralph Tyrrell. Metric regularity properties of monotone mappings. Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 1-8. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a0/