Optimization through dense sets

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...

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Bibliographic Details
Published inBulletin of the Belgian Mathematical Society, Simon Stevin Vol. 23; no. 4; p. 583
Main Authors Jayanarayanan, C.R, Rao, T.S.S.R.K
Format Journal Article
LanguageEnglish
Published Belgian Mathematical Society 01.10.2016
Subjects
Functions (Mathematics)
Mathematical research
Mathematics problems
Vectors (Mathematics)
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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. Key words and phrases : Proximinality, strong proximinality, space of Bochner integrable functions, space of continuous functions.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1480993589