An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones
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 augment...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2025
|
| _version_ | 1824458991658336256 |
|---|---|
| author | Chen, Y Goulart, P |
| author_facet | Chen, Y Goulart, P |
| author_sort | Chen, Y |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2025-02-19T04:34:41Z |
| format | Journal article |
| id | oxford-uuid:64cb50ca-7cd1-4ac2-86f6-53b4d967e8d3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:34:41Z |
| publishDate | 2025 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:64cb50ca-7cd1-4ac2-86f6-53b4d967e8d32025-01-22T20:06:29ZAn Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric ConesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:64cb50ca-7cd1-4ac2-86f6-53b4d967e8d3EnglishJisc Publications RouterSpringer2025Chen, YGoulart, PWe 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. |
| spellingShingle | Chen, Y Goulart, P An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title | An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title_full | An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title_fullStr | An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title_full_unstemmed | An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title_short | An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones |
| title_sort | efficient implementation of interior point methods for a class of nonsymmetric cones |
| work_keys_str_mv | AT cheny anefficientimplementationofinteriorpointmethodsforaclassofnonsymmetriccones AT goulartp anefficientimplementationofinteriorpointmethodsforaclassofnonsymmetriccones AT cheny efficientimplementationofinteriorpointmethodsforaclassofnonsymmetriccones AT goulartp efficientimplementationofinteriorpointmethodsforaclassofnonsymmetriccones |