Abstract
This paper presents and studies the iteration-complexity of a variant of the hybrid proximal extragradient method for solving inclusion problems with strongly (maximal) monotone operators. As applications, we propose and analyze two special cases: variants of the Tseng’s forward–backward method for solving monotone inclusions with strongly monotone and Lipschitz continuous operators and of the Korpelevich extragradient method for solving (strongly monotone) variational inequalities.
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Acknowledgments
M. Marques Alves was partially supported by CNPq Grant Nos. 406250/2013-8, 237068/2013-3 and 306317/2014-1. B. F. Svaiter was partially supported by CNPq Grant Nos. 474996/2013-1, 302962/2011-5 and FAPERJ Grant E-26/201.584/2014.
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Marques Alves, M., Svaiter, B.F. A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis. J Optim Theory Appl 168, 198–215 (2016). https://doi.org/10.1007/s10957-015-0792-y
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DOI: https://doi.org/10.1007/s10957-015-0792-y
Keywords
- Hybrid proximal extragradient method
- Strongly monotone operators
- Variational inequalities
- Tseng’s forward–backward method
- Korpelevich extragradient method