The conjugate of the pointwise maximum of two convex functions revisited
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In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-called Attouch–Brézis regularity condition holds.
KeywordsPointwise maximum Conjugate functions Attouch–Brézis regularity condition
AMS Subject Classification49N15 90C25 90C46
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