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On the employment of inexact restoration for the minimization of functions whose evaluation is subject to errors


Authors: E. G. Birgin, N. Krejić and J. M. Martínez
Journal: Math. Comp. 87 (2018), 1307-1326
MSC (2010): Primary 65K05, 65K10, 90C30, 90C90
DOI: https://doi.org/10.1090/mcom/3246
Published electronically: September 19, 2017
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Abstract: Inexact Restoration is a well established technique for continuous minimization problems with constraints. Recently, it has been used by Krejić and Martínez for optimization of functions whose evaluation is necessarily inexact and comes from an iterative process. This technique will be generalized in the present paper and it will be applied to stochastic optimization and related problems. New convergence results will be given and numerical results will be presented.


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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
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
Email: martinez@ime.unicamp.br

DOI: https://doi.org/10.1090/mcom/3246
Keywords: Inexact Restoration, stochastic programming, global convergence, numerical experiments
Received by editor(s): March 28, 2016
Received by editor(s) in revised form: November 24, 2016
Published electronically: September 19, 2017
Additional Notes: This work was partially supported by the Brazilian agencies FAPESP (grants 2010/10133-0, 2013/03447-6, 2013/05475-7, 2013/07375-0, and 2014/18711-3) and CNPq (grants 309517/2014-1 and 303750/2014-6) and by the Serbian Ministry of Education, Science, and Technological Development (grant 174030)
Article copyright: © Copyright 2017 American Mathematical Society

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