By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that,...The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that, under some conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S] , and under some other conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S].展开更多
基金Supported by the National Natural Science Foundation of China (10571035)
文摘By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
基金Supported by the National Natural Science Foundation of China(69972036)
文摘The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps under Benson proper efficiency. Let W(u) = Pmin[G(u),S],y∧∈W(u∧). It is shown that, under some conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S] , and under some other conditions, DW(u∧,y∧) Pmin[DG(u∧,y∧),S].
