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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A convergence theory for saddle functions

Authors: Hédy Attouch and Roger J.-B. Wets
Journal: Trans. Amer. Math. Soc. 280 (1983), 1-41
MSC: Primary 49A50; Secondary 54A20
MathSciNet review: 712247
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Abstract: We develop a convergence theory called epi/hypo-convergence, for bivariate functions that essentially implies the convergence of their saddle points. We study the properties of this limiting process in particular. We characterize the limit functions associated to any collection of bivariate functions and obtain a compactness theorem for the space of saddle functions. Even when restricted to the univariate case, the results generalize those known for epi-convergence. In particular, we show that the analysis of the convergence process via Yosida approximates must not be restricted to the convex case.

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Article copyright: © Copyright 1983 American Mathematical Society