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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月22日

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  • Yuwen Chen,
  • Paul Goulart

摘要

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.