2 research outputs found
Large-Scale Quadratically Constrained Quadratic Program via Low-Discrepancy Sequences
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.Comment: Accepted at NIPS 2017. arXiv admin note: substantial text overlap
with arXiv:1602.0439
A Distributed Algorithm for High-Dimension Convex Quadratically Constrained Quadratic Programs
We propose a Jacobi-style distributed algorithm to solve convex,
quadratically constrained quadratic programs (QCQPs), which arise from a broad
range of applications. While small to medium-sized convex QCQPs can be solved
efficiently by interior-point algorithms, large-scale problems pose significant
challenges to traditional algorithms that are mainly designed to be implemented
on a single computing unit. The exploding volume of data (and hence, the
problem size), however, may overwhelm any such units. In this paper, we propose
a distributed algorithm for general, non-separable, large-scale convex QCQPs,
using a novel idea of predictor-corrector primal-dual update with an adaptive
step size. The algorithm enables distributed storage of data as well as
parallel distributed computing. We establish the conditions for the proposed
algorithm to converge to a global optimum, and implement our algorithm on a
computer cluster with multiple nodes using Message Passing Interface (MPI). The
numerical experiments are conducted on data sets of various scales from
different applications, and the results show that our algorithm exhibits
favorable scalability for solving large-scale problems