Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Directional quasi/pseudo-normality as sufficient conditions for metric
  subregularity   In this paper we study sufficient conditions for metric subregularity of a
set-valued map which is the sum of a single-valued continuous map and a locally
closed subset. First we derive a sufficient condition for metric subregularity
which is weaker than the so-called first-order sufficient condition for metric
subregularity (FOSCMS) by adding an extra sequential condition. Then we
introduce a directional version of the quasi-normality and the pseudo-normality
which is stronger than the new {weak} sufficient condition for metric
subregularity but is weaker than the classical quasi-normality and
pseudo-normality respectively. Moreover we introduce a nonsmooth version of the
second-order sufficient condition for metric subregularity and show that it is
a sufficient condition for the new sufficient condition for metric
{sub}regularity to hold. An example is used to illustrate that the directional
pseduo-normality can be weaker than FOSCMS. For the class of set-valued maps
where the single-valued mapping is affine and the abstract set is the union of
finitely many convex polyhedral sets, we show that the pseudo-normality and
hence the directional pseudo-normality holds automatically at each point of the
graph. Finally we apply our results to the complementarity and the
Karush-Kuhn-Tucker systems.

4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int