论文标题
双重锥及其比较的概括
Generalizations of doubly nonnegative cones and their comparison
论文作者
论文摘要
在这项研究中，我们检查了双重非负（DNN）锥体的各种扩展，通常用于完全阳性的编程（CPP），以实现比阳性半芬锥的更紧密的放松。为了提供广义CPP（GCPP）的更严格的弛豫，比阳性半圆锥锥体，利用了广义共阳性锥体的内部附近型层次结构，从而从DNN锥获得了两个广义DNN（GDNN）锥。这项研究进行了理论和数值比较，以评估两个GDNN锥体在非负矫正和二阶或二阶或阳性半芬矿锥的直接产物上的松弛强度。这些比较还包括对Burer和Dong提出的现有GDNN锥的分析。解决GCPP问题的几个GDNN编程松弛问题的发现表明，与阳性半芬锥相比，这三个GDNN锥为GCPP提供了明显更紧密的界限。
In this study, we examine the various extensions of the doubly nonnegative (DNN) cone, frequently used in completely positive programming (CPP) to achieve a tighter relaxation than the positive semidefinite cone. To provide tighter relaxation for generalized CPP (GCPP) than the positive semidefinite cone, inner-approximation hierarchies of the generalized copositive cone are exploited to obtain two generalized DNN (GDNN) cones from the DNN cone. This study conducts theoretical and numerical comparisons to assess the relaxation strengths of the two GDNN cones over the direct products of a nonnegative orthant and second-order or positive semidefinite cones. These comparisons also include an analysis of the existing GDNN cone proposed by Burer and Dong. The findings from solving several GDNN programming relaxation problems for a GCPP problem demonstrate that the three GDNN cones provide significantly tighter bounds for GCPP than the positive semidefinite cone.
