Iteration and evaluation complexity for the minimization of functions whose computation is intrinsically inexact
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- by E. G. Birgin, N. Krejić and J. M. Martínez HTML | PDF
- Math. Comp. 89 (2020), 253-278 Request permission
Abstract:
In many cases in which one wishes to minimize a complicated or expensive function, it is convenient to employ cheap approximations, at least when the current approximation to the solution is poor. Adequate strategies for deciding the accuracy desired at each stage of optimization are crucial for the global convergence and overall efficiency of the process. A recently introduced procedure [E. G. Birgin, N. Krejić, and J. M. Martínez, Math. Comp. 87 (2018), 1307–1326, 2018] based on Inexact Restoration is revisited, modified, and analyzed from the point of view of worst-case evaluation complexity in this work.References
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Additional Information
- E. G. Birgin
- Affiliation: Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil
- MR Author ID: 662583
- Email: egbirgin@ime.usp.br
- N. Krejić
- Affiliation: Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia
- Email: natasak@uns.ac.rs
- J. M. Martínez
- Affiliation: Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing (IMECC), University of Campinas, 13083-859 Campinas SP, Brazil
- MR Author ID: 120570
- Email: martinez@ime.unicamp.br
- Received by editor(s): September 25, 2017
- Received by editor(s) in revised form: August 16, 2018, February 11, 2019, and March 6, 2019
- Published electronically: April 25, 2019
- Additional Notes: This work was partially supported by the Brazilian agencies FAPESP (grants 2013/03447-6, 2013/05475-7, 2013/07375-0, 2014/18711-3, and 2016/01860-1) and CNPq (grants 309517/2014-1 and 303750/2014-6) and by the Serbian Ministry of Education, Science, and Technological Development (grant 174030)
- © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 253-278
- MSC (2010): Primary 65K05, 65K10, 90C30, 90C90
- DOI: https://doi.org/10.1090/mcom/3445
- MathSciNet review: 4011542