CONVEXITY AND GLOBAL WELL-POSEDNESS IN SET-OPTIMIZATION

Well-posedness for vector optimization problems has been extensively studied. More recently, some attempts to extend thee results to set-valued optimization have been proposed, mainly applying some scalarization. In this paper we propose a new definition of global well-posedness for set-optimization...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 6; pp. 1897 - 1908
Main Authors Crespi, Giovanni P., Kuroiwa, Daishi, Rocca, Matteo
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2014
Subjects
Convexity
Embeddings
Mathematical functions
Mathematical theorems
Mathematical vectors
Objective functions
Vector spaces
Vector valued functions
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Summary:Well-posedness for vector optimization problems has been extensively studied. More recently, some attempts to extend thee results to set-valued optimization have been proposed, mainly applying some scalarization. In this paper we propose a new definition of global well-posedness for set-optimization problems. Using an embedding technique proposed by Kuroiwa and Nuriya (2006), we prove well-posedness property of a class of generalized convex set-valued maps. 2010Mathematics Subject Classification: 90C29, 90C48, 49J24, 90C31. Key words and phrases: Set-optimization, Global well-posedness, Generalized convexity.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.18.2014.4120