论文标题
增强的SDP松弛，以在Stiefel歧管上进行二次优化
A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold
论文作者
论文摘要
我们研究了半限定的编程（SDP）放松，以在全球优化二次函数上在stiefel歧管上优化二次功能。我们基于文献中的两个想法引入了一种加强的放松：（i）量身定制的SDP，用于带有障碍性黑森的目标； （ii）以及使用Kronecker矩阵产品来构建SDP弛豫。使用四个问题类别上的合成实例，我们表明，通常，我们的放松显着加强了现有的放松，尽管以更长的溶液时间为代价。
We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a tailored SDP for objectives with a block-diagonal Hessian; (ii) and the use of the Kronecker matrix product to construct SDP relaxations. Using synthetic instances on four problem classes, we show that, in general, our relaxation significantly strengthens existing relaxations, although at the expense of longer solution times.
