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

2023/02/14 by Bednarczuk, Ewa M., Bruccola, Giovanni
#90C20 #90C23 #90C26 #90C46 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2302.07004

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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