In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu  and Chalco-Cano et al. . By considering generalized Hukuhara differentiability and generalized convexity (viz. $\eta$-preinvexity, $\eta$-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining ($LS$ and $LU$) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu , Zhang et al.  and Chalco-Cano et al. . To illustrate our theorems suitable examples are also provided.