A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis

Maicon Marques Alves () and B. F. Svaiter ()
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Maicon Marques Alves: Universidade Federal de Santa Catarina
B. F. Svaiter: IMPA

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 1, No 10, 198-215

Abstract: 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.

Keywords: Hybrid proximal extragradient method; Strongly monotone operators; Variational inequalities; Tseng’s forward–backward method; Korpelevich extragradient method; 47H05; 47J20; 90C060; 90C33; 65K10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0792-y

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