Title: Evaluation complexity bounds for smooth constrained nonlinear optimisation using scaled KKT conditions, high-order models and the criticality measure $χ$,
Abstract: 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.