An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones

Yuwen Chen () and Paul Goulart ()
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Yuwen Chen: University of Oxford
Paul Goulart: University of Oxford

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 18, 28 pages

Abstract: Abstract We present an implementation of interior-point methods for generalized power cones, power mean cones and relative entropy cones, by exploiting underlying low-rank and sparsity properties of the Hessians of their logarithmically homogeneous self-concordant barrier functions. We prove that the augmented linear system in our interior-point method can be sparse and quasidefinite after adding a static regularization term, enabling the use of sparse LDL factorization for nonsymmetric cones. Numerical results show that our implementation can exploit sparsity in our test examples.

Keywords: Nonsymmetric cone; Interior-point method; LDL factorization (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02573-5

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