In this paper, we study several existing notions of well- posedness 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.
Miglierina, E., Molho, E., Rocca, M., Well-posedness and scalarization in vector optimization, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2005; 126 (2): 391-409. [doi:10.1007/s10957-005-4723-1] [http://dx.medra.org/10.1007/s10957-005-4723-1] [http://hdl.handle.net/10807/1826]
Well-posedness and scalarization in vector optimization
Miglierina, Enrico;
2005
Abstract
In this paper, we study several existing notions of well- posedness 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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