Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order optimality conditions and Lagrange multiplier
  characterizations of the solution set in quasiconvex programming   Second-order optimality conditions for vector nonlinear programming problems
with inequality constraints are studied in this paper. We introduce a new
second-order constraint qualification, which includes Mangasarian-Fromovitz
constraint qualification as a particular case. We obtain necessary and
sufficient conditions for weak efficiency of problems with a second-order
pseudoconvex vector objective function and quasiconvex constraints. We also
derive Lagrange multiplier characterizations of the solution set of a scalar
problem with a second-order pseudoconvex objective function and quasiconvex
inequality constraints, provided that one of the solutions and the Lagrange
multipliers in the Karush-Kuhn-Tucker conditions are known. At last, we
introduce a notion of a second-order KKT-pseudoconvex problem with inequality
constraints. We derive sufficient and also necessary conditions for efficiency
of second-order KKT-pseudoconvex problems. Three examples are presented.

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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th