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- Title
Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem.
- Authors
Rahman, Md Sadikur; Mahmoud, Emad E.; Shaikh, Ali Akbar; Abdel-Aty, Abdel-Haleem; Bhunia, Asoke Kumar
- Abstract
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.
- Subjects
SADDLEPOINT approximations; NONLINEAR programming; COMPUTER algorithms; NUMERICAL analysis; JOHN, Fritz
- Publication
Computer Systems Science & Engineering, 2021, Vol 38, Issue 3, p351
- ISSN
0267-6192
- Publication type
Article
- DOI
10.32604/csse.2021.015451