A Decomposition Method for Large-scale Convex Quadratically Constrained Quadratic Programs
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We consider solving a convex quadratically constrained quadratic program (QCQP), which has a wide range of applications, including machine learning, data analysis and signal processing. While small to mid-sized convex QCQPs can be solved efficiently by interior-point algorithms, large-scale problems pose significant challenges to traditional centralized algorithms, since the exploding volume of data may overwhelm a single computing unit. In this paper, we propose a decomposition method for general non-separable, large-scale convex QCQPs, using the idea of predictor-corrector proximal primal-dual update with an adaptive step size. The algorithm enables distributed storage of data as well as distributed computing. We both establish convergence of the algorithm to a global optimum and test the algorithm on a computer cluster with multiple threads. The numerical test is done on data sets of different scales using Message Passing Interface, and the results show that our algorithm exhibits favourable scalability for large-scale data even when CPLEX fails to provide a solution due to memory limits.
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