## Abstract

A novel algorithm to solve the quadratic programming (QP) problem over ellipsoids is proposed. This is achieved by splitting the QP problem into two optimisation sub-problems, (1) quadratic programming over a sphere and (2) orthogonal projection.Next, an augmented-Lagrangian algorithm is developed for this multiple constraint optimisation. Benefitting 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 positive semidefinite matrix with a low condition number from the matrices in the quadratic constraint, which is shown to improve convergence of the proposed augmented-Lagrangian algorithm. Finally, applications of the quadratically constrained QP to bounded linear regression and tensor decomposition paradigms are presented.

Original language | English |
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Pages (from-to) | 7097-7120 |

Number of pages | 24 |

Journal | Neural Computing and Applications |

Volume | 32 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

## Keywords

- Generalised eigenvalue decomposition with tucker or tensor train structure
- Linear regression with bound constraint
- Quadratic programming over a single sphere
- Quadratic programming over ellipsoids