In (D. R. Luke, J. Math. Imaging Vision, 47 (2013), 231–238) the structure of the Mordukhovich normal cone to varieties of low-rank matrices at rank-deficient points has been determined. A simplified proof of that result is presented here. As a corollary we obtain the corresponding Clarke normal cone. The results are put into the context of first-order optimality conditions for low-rank matrix optimization problems.
- Matrix optimization
- Low rank constraint
- Optimality conditions
Mathematics Subject Classification (2000)
- Primary 15B99
- 49J52; Secondary 65K10
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Hosseini, S., Luke, D.R., Uschmajew, A. (2019). Tangent and Normal Cones for Low-Rank Matrices. In: Hosseini, S., Mordukhovich, B., Uschmajew, A. (eds) Nonsmooth Optimization and Its Applications. International Series of Numerical Mathematics, vol 170. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-11370-4_3
Publisher Name: Birkhäuser, Cham
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Online ISBN: 978-3-030-11370-4
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