An accelerated augmented Lagrangian method for multi-criteria optimization problem

Xueyong Wang; Yiju Wang; Gang Wang

doi:10.3934/jimo.2018136

Article Contents

2020, Volume 16, Issue 1: 1-9. Doi: 10.3934/jimo.2018136

This issue Previous Article Next Article Fairness preference based decision-making model for concession period in PPP projects

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: November 30, 2016

Revised: October 31, 2017

Early access: September 2018

Published: October 2019

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).

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Abstract

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 $O(1/k)$.

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Mathematics Subject Classification: 15A18, 15A69, 65F15, 65F10.

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