Quadratic Programming Over Ellipsoids (with Applications to Constrained Linear Regression and Tensor Decomposition)
Abstract
A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation sub-problems, quadratic programming over a sphere and orthogonal projection. Next, an augmented-Lagrangian algorithm is developed for this multiple constraint optimisation. Benefit from the fact that the QP over a single sphere can be solved in a closed form by solving a secular equation, we derive a tighter bound of the minimiser of the secular equation. We also propose to generate a new psd matrix with a low condition number from the matrices in the quadratic constraints. This correction method improves convergence of the proposed augmented-Lagrangian algorithm. Finally, applications of the quadratically constrained QP to bounded linear regression and tensor decompositions are presented.
Cite
@article{arxiv.1711.04401,
title = {Quadratic Programming Over Ellipsoids (with Applications to Constrained Linear Regression and Tensor Decomposition)},
author = {Anh-Huy Phan and Masao Yamagishi and Danilo Mandic and Andrzej Cichocki},
journal= {arXiv preprint arXiv:1711.04401},
year = {2017}
}