On G-invex multiobjective programming. Part I. Optimality

Sufficient optimality criteria and duality for multiobjective variational control problems with $$G$$ G -type I objective and constraint functions

“…. , k, is the range of f i (that is, the image of C under f i ) and, therefore, as it follows from the definition of G-invexity introduced by Antczak [3] (see also Definition 5), a function η with respect to which f is G-invex, should be defined as follows η : C × C → R n . Whereas Zhang et al [28] defined any component of a differentiable vector-valued function G f = (G f 1 , .…”

“…, k, can not be the image of C ⊂ R n under f i , since every f i is defined on X × U . As it follows from the above, the definition of a G-invex vector-valued function for a multiobjective variational control problem introduced by Zhang et al [28] is, in some part, the definition of a G-invex vectorvalued function introduced by Antczak [3] for a multiobjective programming problem in finite-dimensional Euclidean space.…”

“…One of a generalization of invexity is the concept of G-invexity introduced by Antczak [2] for scalar optimization problems. In [3,4], Antczak extended the definition of G-invexity to the vectorial case and he used it to prove the necessary and sufficient optimality conditions and duality results for a new class of nonconvex multiobjective programming problems.…”

“…Recently, Khazafi and Rueda [17] extended the concept of V -univexity type I to multiobjective variational programming problems and derived various sufficient optimality conditions and mixed type duality results under generalized V -univexity type I conditions. In this paper, by taking the motivation from Antczak [3,4] and Aghezzaf and Hachimi [1], we introduce the definition of G-type I objective and constraint functions and various concepts of generalized G-type I objective and constraint functions for a multiobjective variational control programming problem with inequality constraints. The class of G-type I objective and constraint functions is a generalization of the class of G-invex functions introduced by Antczak [2] for differentiable vector optimization problems and type I functions introduced by Aghezzaf and Hachimi [1] to the case of a multiobjective variational control programming problem.…”

Optimality conditions for multiobjective programming problems with G-KKT-pseudoinvexity

“…In recent years, Antczak [7] has introduced a new class of vector-valued differentiable functions, which is called G-invex functions. He has established KKT necessary optimality conditions for the class of G-invex multiobjective programming problems.…”