Open Access
november 2016 Optimization through dense sets
C. R. Jayanarayanan, T. S. S. R. K. Rao
Bull. Belg. Math. Soc. Simon Stevin 23(4): 583-594 (november 2016). DOI: 10.36045/bbms/1480993589


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.


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C. R. Jayanarayanan. T. S. S. R. K. Rao. "Optimization through dense sets." Bull. Belg. Math. Soc. Simon Stevin 23 (4) 583 - 594, november 2016.


Published: november 2016
First available in Project Euclid: 6 December 2016

zbMATH: 1357.41028
MathSciNet: MR3579670
Digital Object Identifier: 10.36045/bbms/1480993589

Primary: 41A65
Secondary: 41A50 , 46B20 , 46E40

Keywords: proximinality , space of Bochner integrable functions , space of continuous functions , strong proximinality

Rights: Copyright © 2016 The Belgian Mathematical Society

Vol.23 • No. 4 • november 2016
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