Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Baillon-Haddad Theorem Revisited   In 1977, Baillon and Haddad proved that if the gradient of a convex and
continuously differentiable function is nonexpansive, then it is actually
firmly nonexpansive. This result, which has become known as the Baillon-Haddad
theorem, has found many applications in optimization and numerical functional
analysis. In this note, we propose short alternative proofs of this result and
strengthen its conclusion.

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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: funct-an