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

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 Mathematics Subject Classification (2000) 47H05 · 47J20 · 90C060 · 90C33 · 65K10

• Type: Journal
• Year: 2016
• Where: JOTA
• Authors: Maicon Marques Alves, Benar Fux Svaiter
• Keywords: JOTA 2016