Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order Optimality Conditions by Generalized Derivatives and
  Applications in Hilbert Spaces   In this paper, in terms of three types of generalized second-order
derivatives of a nonsmooth function, we mainly study the corresponding
second-order optimality conditions in a Hilbert space and prove the equivalence
among these optimality conditions for paraconcave functions. As applications,
we use these second-order optimality conditions to study strict local
minimizers of order two and provide sufficient and/or necessary conditions for
ensuring the local minimizer. This work extends and generalizes the study on
second-order optimality conditions from the finite-dimensional space to the
Hilbert space.

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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc