A note on the smoothness of multi-parametric singular value decomposition with applications in optimization
نویسندگان
چکیده
In this paper, we give sufficient conditions for the existence of a smooth singular value decomposition of a multi-parametric matrix function. This smoothness assumption has been considered in the recent paper [R. Behling, G. Haeser, A. Ramos, D. S. Viana, “On a conjecture in nonlinear optimization”, Optimization Online, 2016], where a second-order optimality condition has been proved under a weak, non-constant, rank assumption. Our results, in particular, shows that the result presented in the aforementioned paper generalizes previous known results under stronger assumptions.
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