Multiobjective fractional programming problems and the sufficient condition involving Hb – (p, r)-η- invex function

On the basis of arcwise connected convex functions and (p, r) −η - invex functions, we established Hb –(p, r) –η- invex functions. Based on the generalized invex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and the sufficient optimality condition for the feasible solutions of multiobjective fractional programming problems to be efficient solutions are established and proved.

Duality for multiobjective variational problems under second-order (Ф,ρ)-invexity

The purpose of this article is to introduce the concept of second order (?,?)-invex function for continuous case and apply it to discuss the duality relations for a class of multiobjective variational problem. Weak, strong and strict duality theorems are obtained in order to relate efficient solutions of the primal problem and its second order Mond-Weir type multiobjective variational dual problem using aforesaid assumption. A non-trivial example is also exemplified to show the presence of the proposed class of a function.

Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

<p style='text-indent:20px;'>In this article, we define a new class of functions on Riemannian manifolds, called geodesic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-invex set.</p>

Higher order duality in multiobjective fractional programming problem with generalized convexity

We have introduced higher order generalized hybrid B -(b,?,?,??,?r)-invex function. Then, we have estabilished higher order weak, strong and strict converse duality theorems for a multiobjective fractional programming problem with support function in the numerator of the objective function involving higher order generalized hybrid B -(b,?,?,??,?r)-invex functions. Our results extend and unify several results from the literature.