Bulletin of the Belgian Mathematical Society - Simon Stevin

Optimization through dense sets

C. R. Jayanarayanan and T. S. S. R. K. Rao

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 4 (2016), 583-594.

Dates
First available in Project Euclid: 6 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1480993589

Mathematical Reviews number (MathSciNet)
MR3579670

Zentralblatt MATH identifier
1357.41028

Subjects
Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Secondary: 46E40: Spaces of vector- and operator-valued functions 46B20: Geometry and structure of normed linear spaces 41A50: Best approximation, Chebyshev systems

Keywords
Proximinality strong proximinality space of Bochner integrable functions space of continuous functions

Citation

Jayanarayanan, C. R.; Rao, T. S. S. R. K. Optimization through dense sets. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 4, 583--594. https://projecteuclid.org/euclid.bbms/1480993589


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