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.
Current 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996