An improved distributed dual newton-CG method for convex quadratic programming problems

• This paper considers the problem of solving Programs (QP) arising in the context of distributed optimization and optimal control. A dual decomposition approach is used, where the QP subproblems are solved locally, while the constraints coupling the different subsystems in the time and space domains are enforced by performing a distributed non-smooth Newton iteration on the dual variables. The iterative linear algebra method Conjugate Gradient (CG) is used to compute the dual Newton step. In this context, it has been observed that the dual Hessian can be singular when a poor initial guess for the dual variables is used, hence leading to a failure of the linear algebra. This paper studies this effect and proposes a constraint relaxation strategy to address the problem. It is both formally and experimentally shown that the relaxation prevents the dual Hessian singularity. Moreover, numerical experiments suggest that the proposed relaxation improves significantly the convergence of the Distributed Dual Newton-CG.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

Large scale systems

Hierarchical control

Optimal control

Publication and Content Type

kon (subject category)

ref (subject category)