564 research outputs found

    GMRES-Accelerated ADMM for Quadratic Objectives

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    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 κ\kappa-conditioned problem in O(κ)O(\sqrt{\kappa}) iterations. We give theoretical justification and numerical evidence that the GMRES-accelerated variant consistently solves the same problem in O(κ1/4)O(\kappa^{1/4}) iterations for an order-of-magnitude reduction in iterations, despite a worst-case bound of O(κ)O(\sqrt{\kappa}) 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 O(1/k2)O(1/k^{2}), instead of O(1/k)O(1/k), where kk 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

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    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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