Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
@article{arxiv.1412.0652,
title = {Still Simpler Way of Introducing Interior-Point method for Linear Programming},
author = {Sanjeev Saxena},
journal= {arXiv preprint arXiv:1412.0652},
year = {2015}
}