Which of the following can only be used when training data are linearlyseparable?

Linear hard-margin SVM is designed to find a hyperplane that separates classes with a clear margin and assumes that the data is linearly separable. It aims to maximize the margin while maintaining no training errors, which is only feasible when the data is linearly separable.
Options B, C, and D are not constrained by linear separability:
Option B: linear logistic regression - Logistic regression can be used with both linearly separable and non-linearly separable data.
Option C: linear soft-margin SVM - Soft-margin SVM allows for some misclassifications (errors) and is suitable for non-linearly separable data.
Option D: the centroid method - The centroid method is not specifically designed for linear separability and can be applied to various types of data.
Therefore, the only option that requires linear separability is Option A: linear hard-margin SVM.