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arXiv · 2302.07004

On global solvability of a class of possibly nonconvex QCQP problems in Hilbert spaces

Ewa M. Bednarczuk·Giovanni Bruccola
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Abstract

We provide conditions ensuring that the KKT-type conditions characterizes the global optimality for quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert spaces. The key property is the convexity of a image-type set related to the functions appearing in the formulation of the problem. The proof of the main result relies on a generalized version of the (Jakubovich) S-Lemma in Hilbert spaces. As an application, we consider the class of QCQP problems with a special form of the quadratic terms of the constraints.

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Ewa M. Bednarczuk, Giovanni Bruccola. 2023-02-14. On global solvability of a class of possibly nonconvex QCQP problems in Hilbert spaces. https://arxiv.org/abs/2302.07004

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