Hidden convexity of quadratic systems and its application to quadratic programming
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915739865186304 |
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| author | Huy, Nguyen Quang Hung, Nguyen Huy Van Nghi, Tran Tuan, Hoang Ngoc Van Tuyen, Nguyen |
| author_facet | Huy, Nguyen Quang Hung, Nguyen Huy Van Nghi, Tran Tuan, Hoang Ngoc Van Tuyen, Nguyen |
| contents | In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is established under a newly proposed assumption, which is compared with the previous one in [{\it Math. Program. 147, 171--206, 2014}]. We also provide a complete proof of the hidden convexity of a system of two quadratic functions in [{\it J. Glob. Optim. 56, 1045--1072, 2013}]. Furthermore, necessary and sufficient conditions for the S-lemma concerning systems of quadratic inequalities are investigated. Finally, we derive necessary and sufficient global optimality conditions and strong duality results for quadratic programming. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13511 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hidden convexity of quadratic systems and its application to quadratic programming Huy, Nguyen Quang Hung, Nguyen Huy Van Nghi, Tran Tuan, Hoang Ngoc Van Tuyen, Nguyen Optimization and Control 90C20, 90C26, 90C30, 90C46 In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is established under a newly proposed assumption, which is compared with the previous one in [{\it Math. Program. 147, 171--206, 2014}]. We also provide a complete proof of the hidden convexity of a system of two quadratic functions in [{\it J. Glob. Optim. 56, 1045--1072, 2013}]. Furthermore, necessary and sufficient conditions for the S-lemma concerning systems of quadratic inequalities are investigated. Finally, we derive necessary and sufficient global optimality conditions and strong duality results for quadratic programming. |
| title | Hidden convexity of quadratic systems and its application to quadratic programming |
| topic | Optimization and Control 90C20, 90C26, 90C30, 90C46 |
| url | https://arxiv.org/abs/2601.13511 |