A class of scalarizations of vector optimization problems is studied in order to characterize weakly efficient, efficient, and properly efficient points of a nonconvex vector problem. A parallelism is established between the different solutions of the scalarized problem and the various efficient frontiers. In particular, properly efficient points correspond to stable solutions with respect to suitable perturbations of the feasible set.
Miglierina, E., Molho, E., Scalarizations and its stability in vector optimization, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2002; 114 (3): 657-670. [doi:10.1023/A:1016031214488] [http://hdl.handle.net/10807/1831]
Scalarizations and its stability in vector optimization
Miglierina, Enrico;
2002
Abstract
A class of scalarizations of vector optimization problems is studied in order to characterize weakly efficient, efficient, and properly efficient points of a nonconvex vector problem. A parallelism is established between the different solutions of the scalarized problem and the various efficient frontiers. In particular, properly efficient points correspond to stable solutions with respect to suitable perturbations of the feasible set.
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