Projects per year
Abstract
The worst-case evaluation complexity of finding an approximate first-order critical point using gradient-related non-monotone methods for smooth non-convex and unconstrained problems is investigated. The analysis covers a practical linesearch implementation of these popular methods, allowing for an unknown number of evaluations of the objective function (and its gradient) per iteration. It is shown that this class of methods shares the known complexity properties of a simple steepest-descent scheme and that an approximate first-order critical point can be computed in at most (Formula presented.) function and gradient evaluations, where (Formula presented.) is the user-defined accuracy threshold on the gradient norm.
Original language | English |
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Pages (from-to) | 1349-1361 |
Number of pages | 13 |
Journal | Optimization |
Volume | 64 |
Issue number | 5 |
DOIs | |
Publication status | Published - 4 May 2015 |
Keywords
- evaluation complexity
- linesearch algorithms
- non-linear optimization
- non-monotone methods
- worst-case analysis
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Projects
- 2 Active
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Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research
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Activities
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A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Speaker)
24 Oct 2017Activity: Talk or presentation types › Invited talk
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How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Invited speaker)
5 Feb 2016Activity: Talk or presentation types › Oral presentation
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Polytechnic University of Hong Kong
Philippe Toint (Visiting researcher)
31 Jan 2016 → 14 Feb 2016Activity: Visiting an external institution types › Research/Teaching in a external institution