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arXiv · 2601.13511

Hidden convexity of quadratic systems and its application to quadratic programming

Nguyen Quang Huy·Nguyen Huy Hung·Tran Van Nghi·Hoang Ngoc Tuan·Nguyen Van Tuyen
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Abstract

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.

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Nguyen Quang Huy, Nguyen Huy Hung, Tran Van Nghi, Hoang Ngoc Tuan, Nguyen Van Tuyen. 2026-01-20. Hidden convexity of quadratic systems and its application to quadratic programming. https://arxiv.org/abs/2601.13511

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