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

We show that KKT-type conditions are necessary and sufficient for global optimality for some quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert space. The key property is the convexity of an image-type set, called generalized image set, related to the funct...

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Bibliographic Details
Published in:Optimization 2024-12, Vol.73 (12), p.3537-3556
Main Authors: Bednarczuk, Ewa M., Bruccola, Giovanni
Format: Article
Language:English
Subjects:
Convexity
generalized image set
Global solvability
Hilbert space
KKT conditions
QCQP problems
Quadratic programming
S-lemma
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Summary:We show that KKT-type conditions are necessary and sufficient for global optimality for some quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert space. The key property is the convexity of an image-type set, called generalized image 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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2281640