Abstract
Quadratically Constrained Quadratic Programming (QCQP) is NP-hard in its general non-convex form, but it frequently arises in engineering design and applications ranging from state estimation to beamforming and clustering. Several polynomial-time approximation algorithms exist for non-convex QCQP problems (QCQPs), but their success hinges upon the ability to find at least one feasible point - which is also hard for a general problem instance. In this paper, we present a framework for computing feasible points of general non-convex QCQPs using simple first-order methods. Our approach features low computational and memory requirements, which makes it well-suited for application on large-scale problems. Experiments indicate the empirical effectiveness of our approach, despite currently lacking theoretical guarantees.
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