In this paper, we study several existing notions of wellposedness for vector optimization problems. We separate them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well posed.
Well-posedness and scalarization in vector optimization
MIGLIERINA, ENRICO;MOLHO, ELENA;ROCCA, MATTEO
2005-01-01
Abstract
In this paper, we study several existing notions of wellposedness for vector optimization problems. We separate them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well posed.
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