Shalini Jha

The present article is devoted to multitime multiobjective variational problems via ?-approximation method. In this method, an ?-approximation approach is applied to the considered problem, and a new problem is constructed, called as ?- approximated multitime multiobjective variational problem that contains the change in objective and both constraints functions. The equivalence between an efficient (Pareto optimal) solution to the main multitime multiobjective variational problem is derived along with its associated ?-approximated problem under invexity defined for a multitime functional. Furthermore, we have also discussed the saddle-point criteria for the problem considered and its associated ?-approximated problems via generalized invexity assumptions.

In the paper, a vector optimization problem with twice differentiable functions and cone constraints is considered. The second order modified objective function method is used for solving such a multiobjective programming problem. In this method, for the considered twice differentiable multi-criteria optimization problem, its associated second order vector optimization problem with the modified objective function is constructed at the given arbitrary feasible solution. Then, the equivalence between the sets of (weakly) efficient solutions in the original twice differentiable vector optimization problem with cone constraints and its associated modified vector optimization problem is established. Further, the relationship between an (weakly) efficient solution in the original vector optimization problem and a saddle-point of the second order Lagrange function defined for the modified vector optimization problem is also analyzed.

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

In this paper, a new approach to analyze optimality and saddle‐point criteria for a new class of nonconvex variational problems involving invex functions is studied. Namely, the modified objective function method is used for the considered variational problem in order to characterize its optimal solution. In this method, for the considered variational problem, corresponding modified variational problem with the η‐objective function is constructed. The equivalence in the original variational problem and its associated modified variational problem with the η‐objective function is proved under invexity hypotheses. Furthermore, by using the notion of a Lagrangian function, the connection between a saddle‐point in the modified objective function variational problem and an optimal solution in the considered variational problem is presented. Some examples of nonconvex variational problems are also given to verify the results established in the paper.