Monteiro, Renato D. C.; Svaiter, B. F. On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean. (English) Zbl 1230.90200 SIAM J. Optim. 20, No. 6, 2755-2787 (2010). The authors consider the hybrid proximal extragradient method for finding a zero of a maximal monotone operator and establish its iteration complexity. The developed iteration-complexity analysis is then used to obtain iteration-complexity results for some specific algorithms, namely, Korpelevich’s extragradient method, a particular version of Tseng’s method, and a Newton-type proximal extragradient method. Reviewer: Svetlana A. Kravchenko (Minsk) Cited in 4 ReviewsCited in 72 Documents MSC: 90C60 Abstract computational complexity for mathematical programming problems 90C25 Convex programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 47H05 Monotone operators and generalizations 65K05 Numerical mathematical programming methods 65K10 Numerical optimization and variational techniques 47J20 Variational and other types of inequalities involving nonlinear operators (general) Keywords:extragradient; variational inequality; maximal monotone operator; complexity; complementarity problems; Korpelevich and Newton methods PDFBibTeX XMLCite \textit{R. D. C. Monteiro} and \textit{B. F. Svaiter}, SIAM J. Optim. 20, No. 6, 2755--2787 (2010; Zbl 1230.90200) Full Text: DOI Link