TY - GEN
T1 - Moreau Envelope ADMM for Decentralized Weakly Convex Optimization
AU - Mirzaeifard, Reza
AU - Venkategowda, Naveen K.D.
AU - Jung, Alexander
AU - Werner, Stefan
N1 - Funding Information:
This work was supported by the Research Council of Norway.
Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.
AB - This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.
KW - ADMM
KW - Distributed optimization
KW - Moreau envelope
KW - non-convex and nonsmooth optimization
KW - weakly convex functions
UR - http://www.scopus.com/inward/record.url?scp=85180005100&partnerID=8YFLogxK
U2 - 10.1109/APSIPAASC58517.2023.10317303
DO - 10.1109/APSIPAASC58517.2023.10317303
M3 - Conference article in proceedings
AN - SCOPUS:85180005100
T3 - Proceedings / Asia-Pacific Signal and Information Processing Association Annual Summit and Conference APSIPA ASC
SP - 1126
EP - 1130
BT - 2023 Asia Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2023
PB - IEEE
T2 - Asia-Pacific Signal and Information Processing Association Annual Summit and Conference
Y2 - 31 October 2023 through 3 November 2023
ER -