New optimality conditions and duality results of type in differentiable mathematical programming

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

“…Now, in the natural way, we generalize the definition of a G-invex vector-valued function introduced by Antczak [2] and the definition of differentiable type I multiple objective and constraint functions introduced by Aghezzaf and Hachimi [1] to the case of a multiobjective variational control problem.…”

“…Aghezzaf and Hachimi [1,16] introduced classes of generalized type I functions for a differentiable multiobjective programming problem and derived some Mond-Weir type duality results under the generalized type I assumptions. 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.…”

“…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. Under a variety of G-type I hypotheses, we prove the sufficient optimality conditions for the considered multiobjective variational control programming problem.…”

A note on G-preinvex functions

“…All authors read and approved the final manuscript. 1 Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China.…”

On G-invexity-type nonlinear programming problems

“…In [4], Antczak generalized Hanson's definition of a (differentiable) invex function and he introduced the concept of G-invexity for differentiable constrained optimization problems. He formulated and proved new necessary optimality conditions of G-F. John and G-Karush-KuhnTucker type for differentiable constrained mathematical programming problems and, under Ginvexity assumptions, he established the sufficiency of these necessary optimality conditions.…”