Toward Tractable Conditions for Lower Semicontinuity of Set-Valued Maps: Concepts and Applications

Aussel D.; Bueno O.; Calderón C.; Cotrina J. · Journal of Optimization Theory and Applications (2026) · DOI: 10.1007/s10957-026-02946-y

Resumen

Lower semicontinuity is a key continuity concept in set-valued analysis, but it is also known to be somehow difficult to establish when one wants to tackle specific set-valued maps like constraint maps of quasi-variational inequalities or generalized Nash equilibrium problems or quasi-optimization problems. A classical sufficient condition to obtain the lower semicontinuity is the openness of the graph of the map or of its fibers. Our aim in this work is to propose a weaker concept, called densely locally constant, ensuring the lower semicontinuity and, at the same time, with powerful properties like local intersection property or stability over convexification. Moreover, this new concept allows us to prove alternative selection results, fixed-point theorems and the maximum principle. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

Instituciones: Universidad del Pacífico