An Eigenvalue Decomposition Method for Low-rank and Non-convex Quadratically Constrained Quadratic Programming

The quadratically constrained quadratic programming (QCQP) problems have a wide range of applications and been intensively studied in the fields of information science, control and automation engineering. Currently, one of the main challenge is to solve non-convex QCQP problem efficiently. In certai...

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Bibliographic Details
Published in:IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC) (Online) pp. 558 - 563
Main Authors: Zang, Yanming, Zhu, Hongyan
Format: Conference Proceeding
Language:English
Published: IEEE 03.10.2022
Subjects:
Automation
Computational modeling
eigenvalue decomposition
Eigenvalues and eigenfunctions
low-rank
non-convex
Numerical models
quadratic constrain
Quadratic programming
Simulation
Transforms
ISSN:2689-6621
Online Access:Get full text
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Summary:The quadratically constrained quadratic programming (QCQP) problems have a wide range of applications and been intensively studied in the fields of information science, control and automation engineering. Currently, one of the main challenge is to solve non-convex QCQP problem efficiently. In certain applications, the quadratic constraint coefficient matrix of QCQP problems is exactly or approximately low-rank, which can be utilized to solve the problem. In this work, we study the low-rank non-convex QCQP problems. First, a general optimization proposed. Next, we propose an eigenvalue decomposition based method to transform the low-rank non-convex quadratic constraint into a pair of linear constraints. The computational complexity is then reduced by solving a linearly constrained quadratic programming. Simulation results show that the proposed method outperforms the conventional nonlinear numerical search algorithms for QCQP in terms of optimality and computing time.
ISSN:2689-6621
DOI:10.1109/IAEAC54830.2022.9929567