**Reference:**

M.D. Doan,
M. Diehl,
T. Keviczky, and
B. De Schutter,
"A Jacobi decomposition algorithm for distributed convex optimization
in distributed model predictive control," *Proceedings of the 20th
IFAC World Congress*, Toulouse, France, pp. 4905-4911, July 2017.

**Abstract:**

In this paper we introduce an iterative distributed Jacobi algorithm
for solving convex optimization problems, which is motivated by
distributed model predictive control (MPC) for linear time-invariant
systems. Starting from a given feasible initial guess, the algorithm
iteratively improves the value of the cost function with guaranteed
feasible solutions at every iteration step, and is thus suitable for
MPC applications in which hard constraints are important. The proposed
iterative approach involves solving local optimization problems
consisting of only few subsystems, depending on the flexible choice of
decomposition and the sparsity structure of the couplings. This makes
our approach more applicable to situations where the number of
subsystems is large, the coupling is sparse, and local communication
is available. We also provide a method for checking a posteriori
centralized optimality of the converging solution, using comparison
between Lagrange multipliers of the local problems. Furthermore, a
theoretical result on convergence to optimality for a particular
distributed setting is also provided.

Online version of the paper

@inproceedings{DoaDie:17-006,

author={M.D. Doan and M. Diehl and T. Keviczky and B. {D}e Schutter},

title={A {Jacobi} decomposition algorithm for distributed convex optimization in distributed model predictive control},

booktitle={Proceedings of the 20th IFAC World Congress},

address={Toulouse, France},

pages={4905--4911},

month=jul,

year={2017},

doi={10.1016/j.ifacol.2017.08.744}

}

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