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Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results. (arXiv:2208.03625v1 [math.OC])
Aug. 9, 2022, 1:10 a.m. | Ramtin Madani, Mersedeh Ashraphijuo, Mohsen Kheirandishfard, Alper Atamturk
cs.LG updates on arXiv.org arxiv.org
In the first part of this work [32], we introduce a convex parabolic
relaxation for quadratically-constrained quadratic programs, along with a
sequential penalized parabolic relaxation algorithm to recover near-optimal
feasible solutions. In this second part, we show that starting from a feasible
solution or a near-feasible solution satisfying certain regularity conditions,
the sequential penalized parabolic relaxation algorithm convergences to a point
which satisfies Karush-Kuhn-Tucker optimality conditions. Next, we present
numerical experiments on benchmark non-convex QCQP problems as well as
large-scale …
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