arXiv subjects

Anders Eltved

Publications and source records attributed to Anders Eltved.

2 recordsLinked to original sources

arXiv2021

Strengthened SDP Relaxation for an Extended Trust Region Subproblem with an Application to Optimal Power Flow

We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x - c\| \le b^T x - a$. In particular, we present a class of valid cuts that improve existing semidefinite programming (SDP) relaxations and are separable in polynomial time. We connect our cuts to the literature on the optimal power flow (OPF) problem by demonstrating that previously derived cuts capturing a convex hull important for OPF are actually just special cases of our cuts. In addition, we apply our methodology to derive a new class of closed-form, locally valid, SOC cuts for nonconvex quadratic programs over the mixed polyhedral-conic set $\{x \ge 0 : \| x \| \le 1 \}$. Finally, we show computationally on randomly generated instances that our cuts are effective in further closing the gap of the strongest SDP relaxations in the literature, especially in low dimensions.

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arXiv2019

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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