Large-Scale Quadratically Constrained Quadratic Program via Low-Discrepancy Sequences
This addresses scalability issues in QCQPs for scientific and web domains, but it is incremental as it builds on existing solvers with a transformation technique.
The paper tackles the problem of solving large-scale Quadratically Constrained Quadratic Programs (QCQPs), which are common in scientific and web applications, by developing a method that transforms quadratic constraints into linear forms using low-discrepancy sequences, enabling the use of existing large-scale solvers and demonstrating scalability and improved approximation quality in experiments.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadratic constraint into a linear form by sampling a set of low-discrepancy points. The transformed problem can then be solved by applying any state-of-the-art large-scale quadratic programming solvers. We show the convergence of our approximate solution to the true solution as well as some finite sample error bounds. Experimental results are also shown to prove scalability as well as improved quality of approximation in practice.