Under independence and tail conditions on random symmetric matrices, the DNN relaxation of the standard quadratic program is exact with probability tending to 1, the optimizer is unique and rank one, and recoverable in O(n^2) time.
Zero Duality Gap in Optimal Power Flow Problem
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A hybrid MILP-NLP-complementarity decomposition solved via spatial/temporal ADMM yields up to 13x speedup on unbalanced AC power flow-constrained DES design for networks with 55 loads, with maximum 0.61% optimality gap.
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Exactness of the DNN Relaxation for Random Standard Quadratic Programs
Under independence and tail conditions on random symmetric matrices, the DNN relaxation of the standard quadratic program is exact with probability tending to 1, the optimizer is unique and rank one, and recoverable in O(n^2) time.
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Distributed Energy System Design including Unbalanced AC Power Flow for Large LV Networks with ADMM
A hybrid MILP-NLP-complementarity decomposition solved via spatial/temporal ADMM yields up to 13x speedup on unbalanced AC power flow-constrained DES design for networks with 55 loads, with maximum 0.61% optimality gap.