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 norm (p > 1).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-9,
author = {Shmuel Friedland and Ma\l gorzata Stawiska},
title = {Some approximation problems in semi-algebraic geometry},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {133-147},
zbl = {1338.14055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-9}
}
Shmuel Friedland; Małgorzata Stawiska. Some approximation problems in semi-algebraic geometry. Banach Center Publications, Tome 104 (2015) pp. 133-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-9/