Extending Exact Convex Relaxations of Quadratically Constrained Quadratic Programs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917031071186944 |
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| author | Kojima, Masakazu Kim, Sunyoung Arima, Naohiko |
| author_facet | Kojima, Masakazu Kim, Sunyoung Arima, Naohiko |
| contents | A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the QCQP. Given a QCQP whose convex relaxation is exact, this paper investigates the incorporation of additional quadratic inequality constraints under a non-intersecting quadratic constraint condition while maintaining the exactness of the convex relaxation of the resulting QCQP. Specifically, we extend existing exact semidefinite programming relaxation, completely positive programming relaxation and doubly nonnegative programming relaxation of various classes of QCQPs in a unified manner. Illustrative examples are included to demonstrate the applicability of the established result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Exact Convex Relaxations of Quadratically Constrained Quadratic Programs Kojima, Masakazu Kim, Sunyoung Arima, Naohiko Optimization and Control 90C20, 90C22, 90C25, 90C26 A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the QCQP. Given a QCQP whose convex relaxation is exact, this paper investigates the incorporation of additional quadratic inequality constraints under a non-intersecting quadratic constraint condition while maintaining the exactness of the convex relaxation of the resulting QCQP. Specifically, we extend existing exact semidefinite programming relaxation, completely positive programming relaxation and doubly nonnegative programming relaxation of various classes of QCQPs in a unified manner. Illustrative examples are included to demonstrate the applicability of the established result. |
| title | Extending Exact Convex Relaxations of Quadratically Constrained Quadratic Programs |
| topic | Optimization and Control 90C20, 90C22, 90C25, 90C26 |
| url | https://arxiv.org/abs/2504.03204 |