Optimization through dense sets. (English) Zbl 1357.41028

Jayanarayanan, C. R.; Rao, T. S. S. R. K.

Bull. Belg. Math. Soc. - Simon Stevin 23, No. 4, 583-594 (2016).

Summary: In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions. The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors.

MSC:

41A50	Best approximation, Chebyshev systems
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46B20	Geometry and structure of normed linear spaces

Keywords:

proximinality; strong proximinality; space of Bochner integrable functions; space of continuous functions