On "A Homogeneous Interior-Point Algorithm for Non-Symmetric Convex Conic Optimization"

Understand

In a recent paper, Skajaa and Ye proposed a homogeneous primal-dual interior-point method for non-symmetric conic optimization.

• The authors showed that their algorithm converges to $\varepsilon$-accuracy in $O(\sqrt{\nu}\log \varepsilon^{-1})$ iterations, where $\nu$ is the complexity parameter associated with a barrier function for the primal cone, and thus achieves the best-known iteration complexity for this class of problems.
• However, an earlier result from the literature was used incorrectly in the proofs of two intermediate lemmas in that paper.
• In this note, we propose new proofs of these results, allowing the same complexity bound to be established.