Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evaluation complexity bounds for smooth constrained nonlinear
  optimisation using scaled KKT conditions, high-order models and the
  criticality measure $\chi$   Evaluation complexity for convexly constrained optimization is considered and
it is shown first that the complexity bound of $O(\epsilon^{-3/2})$ proved by
Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an
$\epsilon$-approximate first-order critical point can be obtained under
significantly weaker assumptions. Moreover, the result is generalized to the
case where high-order derivatives are used, resulting in a bound of
$O(\epsilon^{-(p+1)/p})$ evaluations whenever derivatives of order $p$ are
available. It is also shown that the bound of
$O(\epsilon_P^{-1/2}\epsilon_D^{-3/2})$ evaluations ($\epsilon_P$ and
$\epsilon_D$ being primal and dual accuracy thresholds) suggested by Cartis,
Gould and Toint (SINUM, 2015) for the general nonconvex case involving both
equality and inequality constraints can be generalized to a bound of
$O(\epsilon_P^{-1/p}\epsilon_D^{-(p+1)/p})$ evaluations under similarly
weakened assumptions. This paper is variant of a companion report (NTR-11-2015,
University of Namur, Belgium) which uses a different first-order criticality
measure to obtain the same complexity bounds.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int