564 research outputs found
GMRES-Accelerated ADMM for Quadratic Objectives
We consider the sequence acceleration problem for the alternating direction
method-of-multipliers (ADMM) applied to a class of equality-constrained
problems with strongly convex quadratic objectives, which frequently arise as
the Newton subproblem of interior-point methods. Within this context, the ADMM
update equations are linear, the iterates are confined within a Krylov
subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its
ability to accelerate convergence. The basic ADMM method solves a
-conditioned problem in iterations. We give
theoretical justification and numerical evidence that the GMRES-accelerated
variant consistently solves the same problem in iterations
for an order-of-magnitude reduction in iterations, despite a worst-case bound
of iterations. The method is shown to be competitive against
standard preconditioned Krylov subspace methods for saddle-point problems. The
method is embedded within SeDuMi, a popular open-source solver for conic
optimization written in MATLAB, and used to solve many large-scale semidefinite
programs with error that decreases like , instead of ,
where is the iteration index.Comment: 31 pages, 7 figures. Accepted for publication in SIAM Journal on
Optimization (SIOPT
Two-Stage Consensus-Based Distributed MPC for Interconnected Microgrids
In this paper, we propose a model predictive control based two-stage energy
management system that aims at increasing the renewable infeed in
interconnected microgrids (MGs). In particular, the proposed approach ensures
that each MG in the network benefits from power exchange. In the first stage,
the optimal islanded operational cost of each MG is obtained. In the second
stage, the power exchange is determined such that the operational cost of each
MG is below the optimal islanded cost from the first stage. In this stage, a
distributed augmented Lagrangian method is used to solve the optimisation
problem and determine the power flow of the network without requiring a central
entity. This algorithm has faster convergence and same information exchange at
each iteration as the dual decomposition algorithm. The properties of the
algorithm are illustrated in a numerical case study
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