Abstract
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.
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References
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Boţ, R.I., Wanka, G. The conjugate of the pointwise maximum of two convex functions revisited. J Glob Optim 41, 625–632 (2008). https://doi.org/10.1007/s10898-008-9282-1
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DOI: https://doi.org/10.1007/s10898-008-9282-1