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A note on the differentiability of conjugate functions

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Abstract

For a proper, lower semicontinuous and convex function f with Legendre–Fenchel conjugate f *, it is well-known that differentiability properties of f * are equivalent to strict convexity properties of f. In this note a result of this kind is obtained without a convexity assumption on f.

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  1. Department of Mathematics, Luleå University of Technology, 971-87, Luleå, Sweden

    Thomas Strömberg

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  1. Thomas Strömberg
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Correspondence to Thomas Strömberg.

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Strömberg, T. A note on the differentiability of conjugate functions. Arch. Math. 93, 481–485 (2009). https://doi.org/10.1007/s00013-009-0050-3

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  • DOI: https://doi.org/10.1007/s00013-009-0050-3

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