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Projections onto hyperbolas or bilinear constraint sets in Hilbert spaces

Author

Listed:
  • Heinz H. Bauschke

    (University of British Columbia)

  • Manish Krishan Lal

    (University of British Columbia)

  • Xianfu Wang

    (University of British Columbia)

Abstract

Sets of bilinear constraints are important in various machine learning models. Mathematically, they are hyperbolas in a product space. In this paper, we give a complete formula for projections onto sets of bilinear constraints or hyperbolas in a general Hilbert space.

Suggested Citation

  • Heinz H. Bauschke & Manish Krishan Lal & Xianfu Wang, 2023. "Projections onto hyperbolas or bilinear constraint sets in Hilbert spaces," Journal of Global Optimization, Springer, vol. 86(1), pages 25-36, May.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01247-8
    DOI: 10.1007/s10898-022-01247-8
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    References listed on IDEAS

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    1. Veit Elser, 2017. "Matrix product constraints by projection methods," Journal of Global Optimization, Springer, vol. 68(2), pages 329-355, June.
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