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• # Artykuł - szczegóły

## Banach Center Publications

2015 | 107 | 1 | 133-147

## Some approximation problems in semi-algebraic geometry

EN

### Abstrakty

EN
In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We discuss separately the case of the $ℓ^p$ norm (p > 1).

133-147

wydano
2015

### Twórcy

autor
• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA
autor
• Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI 48103-4816, USA