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Compared to modeling problems using the full quantum relative entropy cone, this allows us to remove redundant log-determinant expressions from the barrier function and reduce the overall barrier parameter. Second, we show how certain slices of the quantum relative entropy cone exhibit useful properties which should be exploited whenever possible to perform certain key steps of interior-point methods more efficiently. We demonstrate how these methods can be applied to applications in quantum information theory, including quantifying quantum key rates, quantum rate-distortion functions, quantum channel capacities, and the ground state energy of Hamiltonians. Our numerical results show that these techniques improve computation times by up to several orders of magnitude, and allow previously intractable problems to be solved.<\/jats:p>","DOI":"10.1007\/s12532-025-00296-w","type":"journal-article","created":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T03:11:16Z","timestamp":1763349076000},"page":"481-534","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Interior Point Methods for Structured Quantum Relative Entropy Optimization Problems"],"prefix":"10.1007","volume":"18","author":[{"given":"Kerry","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Saunderson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamza","family":"Fawzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,11,17]]},"reference":[{"key":"296_CR1","doi-asserted-by":"publisher","first-page":"55","DOI":"10.7551\/mitpress\/8996.003.0005","volume-title":"Optimization for Machine Learning","author":"M Andersen","year":"2011","unstructured":"Andersen, M., Dahl, J., Liu, Z., Vandenberghe, L.: Interior-point methods for large-scale cone programming. 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