Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic property of the partial calmness condition for bilevel
  programming problems   The partial calmness for the bilevel programming problem (BLPP) is an
important condition which ensures that a local optimal solution of BLPP is a
local optimal solution of a partially penalized problem where the lower level
optimality constraint is moved to the objective function and hence a weaker
constraint qualification can be applied. In this paper we propose a sufficient
condition in the form of a partial error bound condition which guarantees the
partial calmness condition. We analyse the partial calmness for the combined
program based on the Bouligand (B-) and the Fritz John (FJ) stationary
conditions from a generic point of view. Our main result states that the
partial error bound condition for the combined programs based on B and FJ
conditions are generic for an important setting with applications in economics
and hence the partial calmness for the combined program is not a particularly
stringent assumption. Moreover we derive optimality conditions for the combined
program for the generic case without any extra constraint qualifications and
show the exact equivalence between our optimality condition and the one by
Jongen and Shikhman given in implicit form. Our arguments are based on Jongen,
Jonker and Twilt's generic (five type) classification of the so-called
generalized critical points for one-dimensional parametric optimization
problems and Jongen and Shikhman's generic local reductions of BLPPs.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph