The problem concerned in this paper is the set-valued equation 0 ∈
T(z) where
T is a maximal monotone operator. For given x
k and β
k >: 0, some existing approximate proximal point algorithms take
(x^{k + 1} = tilde x^k ) such that
$x^k + e^k in tilde x^k + beta _k T(tilde x^k ) and left| {e^k } right| leqslant eta _k left| {x^k - tilde x^k } right|,$
where
?k is a non-negative summable sequence. Instead of
(x^{k + 1} = tilde x^k ), the new iterate of the proposing method is given by
$x^{k + 1} = P_Omega [tilde x^k - e^k ],$
where Ω is the domain of
T and PΩ(·) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction sup
K>0 η
Kη1.
