On semi-infinite optimization and Chebyshev approximation with constraints. (English) Zbl 0553.41029
The methods of semi-infinite optimization are used in order to study Chebyshev approximation with constraints. In particular, best approximation by subspaces which do not satisfy the Haar condition is studied. An approximation problem associated with a minimization problem is given. Many of the standard constraints are contained in this approximation problem, e.g. simultaneous Chebyshev approximation, restricted range approximation, bounded coefficients approximation. Then a characterization theorem for best approximations of this problem is given. The result is applied to weak Chebyshev subspaces and weak Markoff subspaces. The best known examples of such subspaces are spaces of spline functions. Moreover, an algorithm is given which computes the best approximations for the above-mentioned problems.
MSC:
| 41A29 | Approximation with constraints |
| 41A50 | Best approximation, Chebyshev systems |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
Keywords:
methods of semi-infinite optimization; Chebyshev approximation with constraints; minimization problem; weak Chebyshev subspaces; weak Markoff subspaces; algorithmReferences:
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