An inertial proximal alternating direction method of multipliers for nonconvex optimization

ABSTRACT

The alternating direction method of multipliers (ADMM) is an efficient method for solving separable problems. However, ADMM may not converge when there is a nonconvex function in the objective. The main contributions of this paper are proposing and analysing an inertial proximal ADMM for a class of nonconvex optimization problems. The proposed algorithm combines the basic ideas of the proximal ADMM and the inertial proximal point method. The global and strong convergence of the proposed algorithm is analysed under mild conditions. Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm.

Keywords:

• Alternating direction method of multipliers
• inertial proximal point method
• Kurdyka–Łojasiewicz property
• nonconvex optimization
• nonsmooth

2010 Mathematics Subject Classifications:

• 90C26
• 90C30

Acknowledgements

The authors would like to thank the anonymous referees for their constructive comments and valuable suggestions which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11601095,11771383), Natural Science Foundation of Guangxi Province (2016GXNSFBA380185,2016GXNSFDA380019).