Quadratic programming over ellipsoids with applications to constrained linear regression and tensor decomposition

Anh Huy Phan, Masao Yamagishi, Danilo Mandic, Andrzej Cichocki

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)7097-7120
    Number of pages24
    JournalNeural Computing and Applications
    Volume32
    Issue number11
    DOIs
    Publication statusPublished - 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

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