Projections onto hyperbolas or bilinear constraint sets in Hilbert spaces

Heinz H. Bauschke (), Manish Krishan Lal () and Xianfu Wang ()
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Heinz H. Bauschke: University of British Columbia
Manish Krishan Lal: University of British Columbia
Xianfu Wang: University of British Columbia

Journal of Global Optimization, 2023, vol. 86, issue 1, No 2, 25-36

Abstract: 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.

Keywords: Bilinear constraint set; Hyperbola; Orthogonal projection; Nonconvex minimization; Prox-regularity; Primary 41A50; 90C26; Secondary 90C20; 46C05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01247-8

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