Large-Scale Quadratically Constrained Quadratic Program via Low-Discrepancy Sequences

TL;DR

This paper introduces a scalable method for large-scale quadratically constrained quadratic programs by transforming quadratic constraints into linear ones using low-discrepancy sampling, enabling efficient solutions with theoretical guarantees.

Contribution

The paper proposes a novel approach that leverages low-discrepancy sequences to approximate quadratic constraints, improving scalability and solution quality for large problems.

Findings

Method converges to true solution with finite sample error bounds

Demonstrates scalability on large problem instances

Shows improved approximation quality in experiments

Abstract

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.