Axiomatic approach to duality in optimization

Nonconvex scalarization in set optimization with set-valued maps

“…This function has been used to separate two nonconvex sets (see [15,16]). We can see that for any y ∈ Y φ e,A (y) = inf a∈A φ e,a (y) .…”

Higher-order Mond–Weir duality for set-valued optimization

“…In [11], Sach et al discussed Mond-Weir-type and Wolfe-type weak duality and strong duality results of set-valued optimization problems under the condition that set-valued mappings satisfy generalized invex properties and by virtue of the codifferential of set-valued mappings introduced in [1]. It should be mentioned that the Lagrangian duality for vector optimization with set-valued mappings in infinite dimensional spaces has been considered in [3][4][5]7,12]. The conjugate duality has been investigated in [15,13].…”

Invex optimisation problems

“…The last section is devoted to duality theory. By making use of the axiomatic approach of [13] (see also [12]) and the generalised Lagrangian approach of [7] (see also [14]), we obtain several Wolfe type duals for invex problems and verify the exactness of duality.…”

“…The very purpose of any duality in optimisation is to construct H and 5 such that (D) is an exact dual of (Po ). Let us first apply the method of [11,13]. For the sake of convenience we consider the problem minima;) (CPo)…”