The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order- s principal submatrix of an order- n covariance matrix. Exact solution methods for this NP-hard problem are based on a branch-and-bound framework. Many of the known upper bounds for the optimal value are based on convex optimization. We present a methodology for “mixing” these bounds to achieve better bounds.

中文翻译：

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最大熵采样的混合凸优化边界

最大熵采样问题是一个基本且具有挑战性的组合优化问题，在空间统计中具有应用。它要求找到 n 阶协方差矩阵的最大行列式主子矩阵。这个 NP-hard 问题的精确求解方法基于分支定界框架。许多已知的最优值上限都是基于凸优化的。我们提出了一种“混合”这些界限以实现更好界限的方法。