A polynomial-based Quadratic Constrained Quadratic Program with Multiple Constraint Sets

Cloud-based control and estimation schemes can substantially reduce on-board computational requirements in autonomous systems, but they also introduce confidentiality and privacy concerns when optimization is delegated to potentially untrusted remote platforms. Within this context, this work investigates the solution of Quadratically Constrained Quadratic Programs (QCQPs) in the presence of multiple ellipsoidal constraint sets. We propose a polynomial-penalty QCQP solver whose iterative procedure relies exclusively on addition and multiplication operations, thereby aligning with the capabilities and limitations of contemporary homomorphic encryption schemes. The effectiveness of the proposed method is demonstrated on a representative numerical example involving a two-dimensional quadratic cost function subject to three quadratic constraints.