0}-A_{0}x_{0},A_{0}x_{0}^{k}-A_{0}x_{0}^{k+0} \bigr\rangle \\ &\qquad{}+\beta\bigl\langle A_{0}x_{0}-A_{0}x_{0}^{k+0},A_{0}x_{0}^{k}-A_{0}x_{0}^{k+0} \bigr\rangle \\ &\quad=\sum_{i=0}^{0}\bigl\langle x_{i}^{k+0}-x_{i}, G_{i} \bigl(x_{i}^{k+0}-x_{i}^{k}\bigr)\bigr\rangle +\bigl\langle Ax^{k+0}-b,-\tilde{\lambda }^{k}\bigr\rangle \\ &\qquad{}+\beta\bigl\langle Ax^{k+0}-b,A_{0}x_{0}^{k}-A_{0}x_{0}^{k+0} \bigr\rangle +\beta\bigl\langle A_{0}x_{0}-A_{0}x_{0}^{k+0},A_{0}x_{0}^{k}-A_{0}x_{0}^{k+0} \bigr\rangle \\ &\quad=\