On equivalence between a variational problem and its modified variational problem with the η‐objective function under invexity
Anurag Jayswal, Tadeusz Antczak, Shalini Duggal Jha · International Transactions in Operational Research · 2017
Abstract 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.