70 research outputs found
Online decentralized decision making with inequality constraints: an ADMM approach
We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we discuss the convergence of the algorithm in an online setting. To be specific, when decisions have to be made sequentially with a fixed time step, there might not be enough time for the ADMM to converge before the scenario changes and the decision needs to be updated. In this case, a suboptimal solution is employed and we analyze the optimality gap given the convergence condition. Moreover, in many cases, the decision making problem changes gradually over time. We propose a warm-start scheme to accelerate the convergence of ADMM and analyze the benefit of the warm-start. The proposed method is demonstrated in a decentralized multiagent control barrier function problem with simulation
Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems
The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this paper we analyze the convergence of the ADMM for solving certain nonconvex consensus and sharing problems. We show that the classical ADMM converges to the set of stationary solutions, provided that the penalty parameter in the augmented Lagrangian is chosen to be sufficiently large. For the sharing problems, we show that the ADMM is convergent regardless of the number of variable blocks. Our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many ADMM variants involving proximal update rules and various flexible block selection rules
Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints
This paper proposes a multiblock alternating direction method of multipliers
for solving a class of multiblock nonsmooth nonconvex optimization problem with
nonlinear coupling constraints. We employ a majorization minimization procedure
in the update of each block of the primal variables. Subsequential and global
convergence of the generated sequence to a critical point of the augmented
Lagrangian are proved. We also establish iteration complexity and provide
preliminary numerical results for the proposed algorithm
An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints
In this paper, we propose an inertial alternating direction method of
multipliers for solving a class of non-convex multi-block optimization problems
with \emph{nonlinear coupling constraints}. Distinctive features of our
proposed method, when compared with other alternating direction methods of
multipliers for solving non-convex problems with nonlinear coupling
constraints, include: (i) we apply the inertial technique to the update of
primal variables and (ii) we apply a non-standard update rule for the
multiplier by scaling the multiplier by a factor before moving along the ascent
direction where a relaxation parameter is allowed. Subsequential convergence
and global convergence are presented for the proposed algorithm
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