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

Abstract

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.

Keywords:

• Global solvability
• QCQP problems
• KKT conditions
• S-lemma
• generalized image set

Mathematics Subject Classifications:

• 90C20
• 90C23
• 90C26
• 90C46

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 861137.