Computing Conjugate Barrier Information for Nonsymmetric Cones
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10957_2022_Article_2076.pdf
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Author(s)
Kapelevich, Lea
Andersen, Erling D.
Vielma, Juan P.
Date Issued
August 20, 2022
Publisher
Springer US
Citation
Kapelevich, Lea, Andersen, Erling D. and Vielma, Juan P. 2022. "Computing Conjugate Barrier Information for Nonsymmetric Cones."
Version
Final published version
Abstract
Abstract
The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1007/s10957-022-02076-1
