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DOI 10.5286/raltr.2015010
Persistent URL http://purl.org/net/epubs/work/23648282
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Record Id 23648282
Title Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
Abstract Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(??3/2) 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 highorder derivatives are used, resulting in a bound of O(??(p+1)/p) evaluations whenever derivatives of order p are available. It is also shown that the bound of O(??1/2 P ??3/2 D ) evaluations (?P and ?D 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(??1/p P ??(p+1)/p D ) evaluations under similarly weakened assumptions.
Organisation STFC , SCI-COMP , SCI-COMP-CM
Funding Information
Related Research Object(s): 44439742
Licence Information: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2015-010. 2015. RAL-TR-2015-010.pdf 2015