TY - JOUR
T1 - Stochastic programming with primal–dual dynamics
T2 - a mean-field game approach
AU - Röling, Casper T.
AU - Ramirez, Stefanny
AU - Bauso, Dario
AU - Tembine, Hamidou
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/8/19
Y1 - 2022/8/19
N2 - This study addresses primal–dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the here and now variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal–dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of the network. Lastly, we emphasize the ways in which penalties on control and state influence the dynamics of agents in the mean-field game.
AB - This study addresses primal–dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the here and now variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal–dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of the network. Lastly, we emphasize the ways in which penalties on control and state influence the dynamics of agents in the mean-field game.
KW - Mean-field games
KW - Network optimization
KW - Primal–dual dynamics
KW - Stochastic programming
UR - http://www.scopus.com/inward/record.url?scp=85136926321&partnerID=8YFLogxK
U2 - 10.1007/s11590-022-01910-9
DO - 10.1007/s11590-022-01910-9
M3 - Article
AN - SCOPUS:85136926321
JO - Optimization letters
JF - Optimization letters
SN - 1862-4472
ER -