The Mathematical Institute, University of Oxford, Eprints Archive

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 $O(\epsilon^{-3/2})$ 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 $O(\epsilon^{-1/2}\ed^{-3/2})$ evaluations ($\epsilon$ and $\ed$ 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 $O(\epsilon^{-1/p}\ed^{-(p+1)/p})$ evaluations under similarly weakened assumptions.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1912
Deposited By: Helen Taylor
Deposited On:24 Oct 2015 08:37
Last Modified:08 Dec 2015 16:09

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