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Abstract
This short note considers and resolves the apparent contradiction between known worst-case complexity results for first- and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre [On Nesterov's smooth Chebyshev-Rosenbrock function, Optim. Methods Softw. (2011)] implying a very large lower bound on the number of iterations required to reach the solution's neighbourhood for a specific problem with variable dimension.
| Original language | English |
|---|---|
| Pages (from-to) | 451-457 |
| Number of pages | 7 |
| Journal | Optimization Methods and Software |
| Volume | 28 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jun 2013 |
Keywords
- evaluation complexity
- nonconvex optimization
- worst-case analysis
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Evaluation complexity of algorithms for nonconvex optimization
Cartis, C., Gould, N. I. M. & TOINT, P., Jul 2022, SIAM. 600 p. (SIAM-MOS Series on Optimization)Research output: Book/Report/Journal › Book
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Adaptive regularization algorithms with inexact evaluations for nonconvex optimization
Bellavia, S., Gurioli, G., Morini, B. & Toint, P., 2 Jan 2020, In: SIAM Journal on Optimization. 29, 4, p. 2881-2915 35 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile38 Downloads (Pure) -
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
Cartis, C., Gould, N. I. M. & Toint, P., Jun 2019, Springer Optimization and Its Applications: Algorithms, Complexity and Applications. Demetriou, I. & Pardalos, P. (eds.). Springer Heidelberg, p. 5-26 22 p. (Springer Optimization and Its Applications; vol. 145).Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter
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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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
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How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Speaker)
31 Jan 2016Activity: Talk or presentation types › Oral presentation