Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abadie condition for infinite programming problems under Relaxed
  Constant Rank Constraint Qualification Plus   We consider systems of infinite number of inequalities and equations given by
continuously differentiable functions defined on Banach spaces with values in
Hilbert spaces. We represent these systems with the help of coefficients, in a
given Schauder basis. We prove that Abadie condition (linearized cone is
contained in tangent cone) holds. The main tools are: new infinite-dimensional
Relaxed Constant Rank Condition Plus (inspired by the finite-dimensional idea
of Minchenko and Stakhovski), Rank Theorem and Ljusternik Theorem.

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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th