论文标题
加强了扩展信任区域子问题的SDP放松，并应用了最佳功率流量
Strengthened SDP Relaxation for an Extended Trust Region Subproblem with an Application to Optimal Power Flow
论文作者
论文摘要
我们研究了一个扩展信任区域子问题，将空心球$ r \ le \ | x \ |上的非凸函数最小化。 \ le r $与表格$ \ | x -c \ |的全维二阶锥（SOC）约束相交\ le b^t x- $。特别是，我们提出了一类有效切割，以改善现有的半决赛编程（SDP）放松，并且在多项式时间内可分开。我们通过证明先前派生的切割捕获凸面船体对OPF很重要的剪辑实际上只是我们切割的特殊情况，将削减与有关最佳功率流（OPF）问题的文献联系起来。此外，我们应用我们的方法来得出一类新的封闭形式的，本地有效的，在混合多面体式套件上的非凸二次程序$ \ \ \ {x \ ge 0：\ |上的非convex二次程序的SOC削减。 x \ | \ le 1 \} $。最后，我们对随机生成的实例进行了计算，即我们的削减有效地缩小了文献中最强的SDP松弛的差距，尤其是在低维度中。
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.
