 as $$\documentclass[00pt]{minimal}                 \usepackage{amsmath}                 \usepackage{wasysym}                  \usepackage{amsfonts}                  \usepackage{amssymb}                  \usepackage{amsbsy}                 \usepackage{mathrsfs}                 \usepackage{upgreek}                 \setlength{\oddsidemargin}{-00pt}                 \begin{document} $$\begin{aligned} 0={}&\bigl\langle x_{0}^{k+0}-x_{0}, \nabla\theta_{0}\bigl(x_{0}^{k+0}\bigr)\bigr\rangle +\bigl\langle x_{0}^{k+0}-x_{0}, G_{0}\bigl(x_{0}^{k+0}-x_{0}^{k} \bigr)+\beta A_{0}^{\top}A_{0}\bigl(x_{0}^{k}-x_{0}^{k+0} \bigr)\bigr\rangle \\ &{} +\bigl\langle A_{0}\bigl(x_{0}^{k+0}-x_{0} \bigr),-\tilde{\lambda}^{k}\bigr\rangle \\ \geq{}&\theta_{0}\bigl(x_{0}^{k+0}\bigr)- \theta_{0}(x_{0})+\bigl\langle x_{0}^{k+0}-x_{0}, G_{0}\bigl(x_{0}^{k+0}-x_{0}^{k} \bigr)+\beta A_{0}^{\top}A_{0}\bigl(x_{0}^{k}-x_{0}^{k+0} \bigr)\bigr\rangle \\ &{} +\bigl\langle A_{0}\bigl(x_{0}^{k+0}-x_{0} \bigr),-\tilde{\lambda}^{k}\bigr\rangle , \end{aligned}$$ \end{document}$$ where the inequality comes from the convexity of $\documentclass[00pt]{minimal}                 \usepackage{amsmath}                 \usepackage{wasysym}                  \usepackage{amsfonts}                  \usepackage{amssymb}                  \usepackage{amsbsy}                 \usepackage{mathrsfs}                 \usepackage{upgreek}                 \setlength{\oddsidemargin}{-00pt}                 \begin{document}$\theta_{0}(\cdot)$\end{document}$ and ([0](#Equ0){ref-type=""}). 