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arXiv · 2604.02968

Separable QCQPs and Their Exact SDP Relaxations

Masakazu Kojima·Sunyoung Kim·Naohiko Arima
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Abstract

This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show that exactness is preserved when such QCQPs are combined through a separable horizontal connection, where the coupling is induced through the right-hand-side parameters of the constraints. The proposed framework provides a simple sufficient condition for exactness of the resulting SDPR. We then identify notable classes of QCQPs for which this condition holds, including convex QCQPs, QCQPs defined by sign-pattern and graph-structural conditions, and separable homogeneous QCQPs with a limited number of constraints. Two examples illustrate the constructive nature of the proposed framework, showing how heterogeneous QCQPs can be combined to yield new instances with exact SDP relaxations.

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Masakazu Kojima, Sunyoung Kim, Naohiko Arima. 2026-04-03. Separable QCQPs and Their Exact SDP Relaxations. https://arxiv.org/abs/2604.02968

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