# Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models

Cartis, Coralia and Gould, Nicholas I. M. and Toint, Philippe L. (2015) Evaluation complexity bounds
for smooth constrained nonlinear optimization
using scaled KKT conditions and high-order models.
Technical Report. Unspecified. (Submitted)

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## Abstract

Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an -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 evaluations whenever derivatives of order are available. It is also shown that the bound of evaluations ( and being primal and dual accuracy thresholds) suggested by Cartis, Gould and Toint (SINUM, 53(2), 2015, pp.836-851) for the general nonconvex case involving both equality and inequality constraints can be generalized to yield a bound of evaluations under similarly weakened assumptions.

Item Type: Technical Report (Technical Report) H - N > Numerical analysis Numerical Analysis Group 1912 Helen Taylor 24 Oct 2015 08:37 08 Dec 2015 16:09

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