Multitime multiobjective variational problems via $\eta$-approximation method

Abstract

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