On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Understand

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods.

• The study of the convergence properties of these methods is in general difficult due to the nonconvexity of the problem.
• In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated.
• The first method is adapted from the classic quadratic penalty function method and is called the Alternating Direction Penalty Method (ADPM).