New insights into the NLP-Id bound for maximum-entropy sampling

We establish new properties of the NLP-Id upper bound for the maxi\-mum-entropy sampling problem (MESP). In particular, we give a detailed look at the concavity of its objective function as a function of the scaling parameter employed for NLP bounds for MESP. This leads to more relaxed choices for the scaling parameter for NLP-Id and even improved upper bounds for MESP.