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.
Convexity and global well-posedness in set-optimization
CRESPI, GIOVANNI PAOLO;ROCCA, MATTEO
2014-01-01
Abstract
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.
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