Abstract
In this paper, by using the invexity (or pseudoinvexity) and Frechet differentiability of some integral functionals of curvilinear type, we state some relations between the solutions of a new non-linear optimization problem and the associated variational inequality. In order to prove the results derived in this paper, we use the new notion of invex set by considering some given functions. To justify the effectiveness and outstanding applicability of this work, some illustrative examples are provided.