Optimality Conditions for Invex Interval Valued Nonlinear Programming Problems Involving Generalized $H$-Derivative

Izhar Ahmad, Deepak Singh, Bilal Ahmad Dar

In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. 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 [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided.