Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces. (English) Zbl 1427.90233
Summary: A new class of generalized convex set-valued maps termed relatively solid generalized cone-subconvexlike maps is introduced in real linear spaces not equipped with any topology. This class is a generalization of generalized cone-subconvexlike maps and relatively solid cone-subconvexlike maps. Necessary and sufficient conditions for Benson proper efficiency of set-valued optimization problem are established by means of scalarization, Lagrange multipliers, saddle points and duality. The results generalize and improve some corresponding ones in the literature. Some examples are afforded to illustrate our results.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 90C30 | Nonlinear programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
Keywords:
set-valued maps; relative algebraic interior; vector closure; Benson proper efficiency; generalized cone subconvexlikenessReferences:
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