The Complexity of Computing KKT Solutions of Quadratic Programs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918105771409408 |
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| author | Fearnley, John Goldberg, Paul W. Hollender, Alexandros Savani, Rahul |
| author_facet | Fearnley, John Goldberg, Paul W. Hollender, Alexandros Savani, Rahul |
| contents | It is well known that solving a (non-convex) quadratic program is NP-hard. We show that the problem remains hard even if we are only looking for a Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove that computing a KKT point of a quadratic polynomial over the domain $[0,1]^n$ is complete for the class CLS = PPAD$\cap$PLS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13738 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Complexity of Computing KKT Solutions of Quadratic Programs Fearnley, John Goldberg, Paul W. Hollender, Alexandros Savani, Rahul Computational Complexity Optimization and Control It is well known that solving a (non-convex) quadratic program is NP-hard. We show that the problem remains hard even if we are only looking for a Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove that computing a KKT point of a quadratic polynomial over the domain $[0,1]^n$ is complete for the class CLS = PPAD$\cap$PLS. |
| title | The Complexity of Computing KKT Solutions of Quadratic Programs |
| topic | Computational Complexity Optimization and Control |
| url | https://arxiv.org/abs/2311.13738 |