On best approximation by nonconvex sets and perturbation of nonconvex inequality systems in Hilbert spaces. (English) Zbl 1051.41018
Summary: By virtue of convexification techniques, we study best approximations to a closed set \(C\) in a Hilbert space as well as perturbation conditions relative to \(C\) and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.
MSC:
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 41A29 | Approximation with constraints |
