Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of the optimal values under small perturbations of the
  constraint set   This paper discusses a general and useful stability principle which, roughly
speaking, says that given a uniformly continuous function defined on an
arbitrary metric space, if the function is bounded on the constraint set and we
slightly change this set, then its optimal (extreme) values on this set vary
slightly, and, moreover, they are actually uniformly continuous as a function
of the constraint set. The principle holds in a much more general setting than
a metric space, since the distance function may be asymmetric, may attain
negative and even infinite values, and so on. This stability principle leads to
applications in parametric optimization, mixed linear-nonlinear programming and
analysis of Lipschitz continuity, as well as to a general scheme for tackling a
wide class of non-convex and non-smooth optimization problems. We also discuss
the issue of stability when the objective function is merely continuous. As a
byproduct of our analysis we obtain a significant generalization of the concept
of a generalized inverse of a linear operator and a very general variant of the
so-called "Hoffman's Lemma".

13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics