# American Institute of Mathematical Sciences

January  2020, 16(1): 1-9. doi: 10.3934/jimo.2018136

## An accelerated augmented Lagrangian method for multi-criteria optimization problem

 School of Management Science, Qufu Normal University, Rizhao Shandong, 276800, China

1This research was done during his postdoctoral period in Qufu Normal Univeristy

Received  December 2016 Revised  November 2017 Published  September 2018

Fund Project: This work was supported by the Natural Science Foundation of China (11671228, 11801309), Shandong Provincial Natural Science Foundation (ZR2016AM10), and Science & Technology Planning Project of Qufu Normal University (XKJ201623).

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 $O(1/k^2)$ which improves the original ALM whose iteration-complexity is $O(1/k)$.

Citation: Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 1-9. doi: 10.3934/jimo.2018136
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##### References:
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