Abstract
We investigate conditions under which the weakly efficient set for minimization of m objective functions on a closed and convex X⊂ R d (m> d) is fully determined by the weakly efficient sets for all n-objective subsets for some n< m. For quasiconvex functions, it is their union with n= d+ 1. For lower semi-continuous explicitly quasiconvex functions, the weakly efficient set equals the linear enclosure of their union with n= d, as soon as it is bounded. Sufficient conditions for the weakly efficient set to be bounded or unbounded are also investigated.
Original language | English |
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Pages (from-to) | 547–564 |
Number of pages | 18 |
Journal | Journal of Optimization Theory and Applications |
Volume | 184 |
Issue number | 2 |
DOIs | |
Publication status | Published - 7 Dec 2019 |
Keywords
- Weakly efficient set
- Quasiconvex functions
- Multiobjective
- Helly’s theorem
- Linear enclosure