Projects per year
Abstract
Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(ε ^{−3∕2} ) proved by Cartis et al. (IMA J Numer Anal 32:1662–1695, 2012) for computing an εapproximate firstorder critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where highorder derivatives are used, resulting in a bound of (Formula presented) evaluations whenever derivatives of order p are available. It is also shown that the bound of (Formula presented) evaluations (ε _{P} and ε _{D} being primal and dual accuracy thresholds) suggested by Cartis et al. (SIAM J. Numer. Anal. 53:836–851, 2015) for the general nonconvex case involving both equality and inequality constraints can be generalized to yield a bound of (Formula presented) evaluations under similarly weakened assumptions.
Original language  English 

Title of host publication  Springer Optimization and Its Applications 
Subtitle of host publication  Algorithms, Complexity and Applications 
Editors  Iannis Demetriou, Panos Pardalos 
Publisher  Springer Heidelberg 
Chapter  1 
Pages  526 
Number of pages  22 
ISBN (Electronic)  9783030127664 
DOIs  
Publication status  Published  Jun 2019 
Publication series
Name  Springer Optimization and Its Applications 

Volume  145 
ISSN (Print)  19316828 
ISSN (Electronic)  19316836 
Keywords
 Complexity theory
 Nonlinear optimization
 scaled optimality conditions
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Projects
 2 Active

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research

Activities

Oxford University
Philippe Toint (Visiting researcher)
20 Nov 2019 → 6 Dec 2019Activity: Visiting an external institution types › Visiting an external academic institution

A path and some adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
24 Oct 2017Activity: Talk or presentation types › Invited talk

A path and some adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
23 Oct 2017Activity: Talk or presentation types › Invited talk