Abstract
Using the notion of Hausdorff lower semi-continuity (or of Hausdorff-bounded lower semi-continuity) for relations in product spaces, we give simple conditions ensuring that the intersection of two lower semi-continuous relations, not necessarily both with convex values, is an other one. Then we apply the preceeding results to pairs of functions-constraints. That allows us to give conditions of stability in some problems of saddle-points with constraints.
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© 1992 Springer-Verlag Berlin Heidelberg
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Guillerme, J. (1992). Intersections of lower semi-continuous relations. Applications to the stability of constrained saddle points. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_9
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DOI: https://doi.org/10.1007/978-3-642-51682-5_9
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