Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identifying Activity   Identification of active constraints in constrained optimization is of
interest from both practical and theoretical viewpoints, as it holds the
promise of reducing an inequality-constrained problem to an
equality-constrained problem, in a neighborhood of a solution. We study this
issue in the more general setting of composite nonsmooth minimization, in which
the objective is a composition of a smooth vector function c with a lower
semicontinuous function h, typically nonsmooth but structured. In this setting,
the graph of the generalized gradient of h can often be decomposed into a union
(nondisjoint) of simpler subsets. "Identification" amounts to deciding which
subsets of the graph are "active" in the criticality conditions at a given
solution. We give conditions under which any convergent sequence of approximate
critical points finitely identifies the activity. Prominent among these
properties is a condition akin to the Mangasarian-Fromovitz constraint
qualification, which ensures boundedness of the set of multiplier vectors that
satisfy the optimality conditions at the solution.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex