Abstract In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient are proved for such nonconvex smooth vector optimization problems. Further, duals in sense Mond–Weir defined considered and several duality re...

A multiobjective variational problem involving higher order derivatives is considered and optimality conditions for this problem are derived. A Mond-Weir type dual to this problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the al...

New concepts of generalized ρ, θ -η invex functions for non-differentiable functions and generalized ρ, θ -η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized ρ, θ -η invexity of functions and generalized ρ, θ -η invariant monotonicity of the corresponding Clarke’s subdifferentials are studied. Some of our results are extension and improv...

The exactness of the penalization for the exact l1 penalty function method used for solving nonsmooth constrained optimization problems with both inequality and equality constraints are presented. Thus, the equivalence between the sets of optimal solutions in the nonsmooth constrained optimization problem and its associated penalized optimization problem with the exact l1 penalty function is es...

In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be a LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond-Weir type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point ty...

<p style='text-indent:20px;'>In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems with <inline-formula><tex-math id="M4">\begin{document}$ E $\end{document}</tex-math></inline-formula>-differentiable functions. Namely, an id="M5">\begin{document}$ vector-valued function, the id="M6"&g...