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On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean. (English) Zbl 1230.90200

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.

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)
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