Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

摘要

The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem. To achieve the study objective, we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem. Also, we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems. After that, we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem. Next, we have shown that both the saddle point conditions (Fritz-John and Kuhn-Tucker) are sufficient without any convexity requirements. Then with the convexity requirements, we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints. Here, all the results are derived with the help of interval order relations. Finally, we illustrate all the results with the help of a numerical example.