Modi ed objective function approach for multitime variational problems

Abstract

The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate the results established in the paper.