249 research outputs found
An Algorithm for Nonsymmetric Conic Optimization Inspired by MOSEK
We analyze the scaling matrix, search direction, and neighborhood used in
MOSEK's algorithm for nonsymmetric conic optimization [Dahl and Andersen,
2019]. It is proven that these can be used to compute a near-optimal solution
to the homogeneous self-dual model in polynomial time.Comment: 29 page
On the Robustness and Scalability of Semidefinite Relaxation for Optimal Power Flow Problems
Semidefinite relaxation techniques have shown great promise for nonconvex
optimal power flow problems. However, a number of independent numerical
experiments have led to concerns about scalability and robustness of existing
SDP solvers. To address these concerns, we investigate some numerical aspects
of the problem and compare different state-of-the-art solvers. Our results
demonstrate that semidefinite relaxations of large problem instances with on
the order of 10,000 buses can be solved reliably and to reasonable accuracy
within minutes. Furthermore, the semidefinite relaxation of a test case with
25,000 buses can be solved reliably within half an hour; the largest test case
with 82,000 buses is solved within eight hours. We also compare the lower bound
obtained via semidefinite relaxation to locally optimal solutions obtained with
nonlinear optimization methods and calculate the optimality gap
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