We analyze the scaling matrix, search direction, and neighborhood used in MOSEK's algorithm for nonsymmetric conic optimization [Dahl and Andersen, 2019]. It is proven that these can be used to compute a near-optimal solution to the homogeneous self-dual model in polynomial time.
@article{arxiv.2003.01546,
title = {An Algorithm for Nonsymmetric Conic Optimization Inspired by MOSEK},
author = {Riley Badenbroek and Joachim Dahl},
journal= {arXiv preprint arXiv:2003.01546},
year = {2020}
}