An accelerated augmented Lagrangian method for multi-criteria optimization problem

Abstract

<p style='text-indent:20px;'>By virtue of the Nesterov's acceleration technique, we establish an accelerated augmented Lagrangian method for solving linearly constrained multi-criteria optimization problem. For this method, we establish its global convergence under suitable condition. Further, we show that its iteration-complexity is <inline-formula><tex-math id="M1">\begin{document}$O(1/k^2)$\end{document}</tex-math></inline-formula> which improves the original ALM whose iteration-complexity is <inline-formula><tex-math id="M2">\begin{document}$O(1/k)$\end{document}</tex-math></inline-formula>.