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Inexact Restoration approach for minimization with inexact evaluation of the objective function


Authors: Nataša Krejić and J. M. Martínez
Journal: Math. Comp. 85 (2016), 1775-1791
MSC (2010): Primary 65K05, 65K10, 90C30, 90C90
DOI: https://doi.org/10.1090/mcom/3025
Published electronically: September 9, 2015
MathSciNet review: 3471107
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Abstract: A new method is introduced for minimizing a function that can be computed only inexactly, with different levels of accuracy. The challenge is to evaluate the (potentially very expensive) objective function with low accuracy as far as this does not interfere with the goal of getting high accuracy minimization at the end. For achieving this goal the problem is reformulated in terms of constrained optimization and handled with an Inexact Restoration technique. Convergence is proved and numerical experiments motivated by Electronic Structure Calculations are presented, which indicate that the new method overcomes current approaches for solving large-scale problems.


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Additional Information

Nataša 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/3025
Keywords: Inexact Restoration, inexact evaluations, global convergence, numerical experiments
Received by editor(s): May 8, 2014
Received by editor(s) in revised form: November 6, 2014, and December 8, 2014
Published electronically: September 9, 2015
Additional Notes: The first author’s research was supported by the Serbian Ministry of Education, Science, and Technological Development, Grant no. 174030
The second author’s research was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo under projects CEPID-Cemeai on Industrial Mathematics 2013/07375-0 and PT 2006/53768-0, and CNPq under projects 300933-2009-6 and 400926-2013-0
Article copyright: © Copyright 2015 American Mathematical Society