In this paper, we suggest and analyze both explicit and implicit iterative schemes for two strongly positive operators and a nonexpansive mapping S on a Hilbert space. We also study explicit and implicit versions of iterative schemes for an inverse-strongly monotone mapping T and S by an extragradient-like approximation method. The viscosity approximation methods are employed to establish stron...

In this paper, we introduce regularization methods for finding a point, being not only solution monotone variational inequality problem but also common zero an infinite family of inverse strongly non-self operators closed convex subset in real Hilbert space. these methods, finite number the is used at each iteration step. Applications to fixed point strictly pseudo-contractive and split feasibi...

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well some theories have proved high efficiency LISTA for solving sparse coding problems. However, existing methods are all serial connection. To address this issue, we propose a novel extragradient based (ELISTA), which residual structure and th...

In this paper, we propose a new approximate proximal point algorithm (APPA). The proposed method uses a new searching direction which differs from the other existing APPAs. Under some mild conditions, we show that the proposed method is globally convergent. The results presented in this paper extend and improve some well-known results in the literature.

In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize f...

In this paper, we consider a rst-order block-decomposition method for minimizing the sum of a convex di erentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for ...