Title :
On Distributed Convex Optimization Under Inequality and Equality Constraints
Author :
Zhu, Minghui ; Martínez, Sonia
Author_Institution :
Dept. of Mech. & Aerosp. Eng., Univ. of California at San Diego, La Jolla, CA, USA
Abstract :
We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater´s condition.
Keywords :
convex programming; minimisation; multi-agent systems; multi-robot systems; set theory; Lagrangian functions; Slater condition; distributed convex optimization; distributed primal-dual subgradient algorithms; global constraint set; global equality constraint; global inequality constraint; global objective function minimization; local constraint set intersection; multiagent convex optimization problem; penalty functions; saddle points; standard connectivity property; Algorithm design and analysis; Convergence; Convex functions; Heuristic algorithms; Lagrangian functions; Network topology; Optimization; Cooperative control; distributed optimization; multi-agent systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2167817