2021/12/28 by Zhong‐Zhu Chen, Chen, Zhongzhu, Marcia Fampa +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Adversarial Robustness in Machine Learning #FOS: Mathematics #Optimization and Control (math.OC) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2112.14291
openalex publication_date 2021/12/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/01
Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this factorization bound is invariant under scaling and also independent of the particular factorization chosen. We give a variable-fixing methodology that could be used in a branch-and-bound scheme based on the factorization bound for exact solution of CMESP. We report on successful experiments with a commercial nonlinear-programming solver. We further demonstrate that the known "mixing" technique can be successfully used to combine the factorization bound with the factorization bound of the complementary CMESP, and also with the "linx bound" of Anstreicher (2020).