Quadratic Programming Over Ellipsoids (with Applications to Constrained Linear Regression and Tensor Decomposition)

Anh-Huy Phan; Masao Yamagishi; Danilo Mandic; Andrzej Cichocki

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arXiv · 1711.04401

Quadratic Programming Over Ellipsoids (with Applications to Constrained Linear Regression and Tensor Decomposition)

Anh-Huy Phan·Masao Yamagishi·Danilo Mandic·Andrzej Cichocki

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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.

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Anh-Huy Phan, Masao Yamagishi, Danilo Mandic, Andrzej Cichocki. 2017-11-13. Quadratic Programming Over Ellipsoids (with Applications to Constrained Linear Regression and Tensor Decomposition). https://arxiv.org/abs/1711.04401

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