论文标题
约旦对称性减少了双圆锥锥体优化的锥形优化：理论和软件
Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: theory and software
论文作者
论文摘要
多项式优化问题（POP）的一种常见计算方法是使用（层次结构）半决赛编程（SDP）弛豫。当需要POP中的变量为非负数时，这些SDP问题通常涉及非负矩阵，即它们是偶有的非负锥体上的圆锥优化问题。帕里洛（Parrilo）和佩门师（Permenter）最近引入了约旦（Jordan）还原是一种用于锥形优化的对称性降低方法[数学编程181（1），2020年]。我们将此方法扩展到双重的非负锥，并研究其在已知的二次分配和最大稳定集问题的已知放松中的应用。我们还介绍了新的Julia软件，其中减少了对称性。
A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in the POP are required to be nonnegative, these SDP problems typically involve nonnegative matrices, i.e. they are conic optimization problems over the doubly nonnegative cone. The Jordan reduction, a symmetry reduction method for conic optimization, was recently introduced for symmetric cones by Parrilo and Permenter [Mathematical Programming 181(1), 2020]. We extend this method to the doubly nonnegative cone, and investigate its application to known relaxations of the quadratic assignment and maximum stable set problems. We also introduce new Julia software where the symmetry reduction is implemented.
