### Dang Doan (Universität Freiburg, Germany)

#### A distributed Jacobi algorithm for large-scale constrained convex optimization

*Tuesday 25 July 2017 at 14.00, JCMB 6206*

##### Abstract

We consider a sparse convex optimization problem that involves a group of
agents, under general affine constraints. This problem often arises in
distributed model predictive control applications. A distributed Jacobi
algorithm is proposed to solve this problem in a cooperative manner. In every
iteration, each agent solves its local problem and exchanges information with
its 'direct neighbours'. After that, the new and the old solutions are used in
a convex combination to maintain feasibility at every iteration. The convex
combination update can also be carried out locally.

We provide the a posteriori certification for centralized optimality of
distributed solutions, based on comparing Lagrange multipliers of the local
problems. Furthermore, we also prove a priori conditions that guarantee
convergence to optimality in several problem settings.

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