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

Md Sadikur Rahman1, Emad E. Mahmoud2, Ali Akbar Shaikh1,*, Abdel-Haleem Abdel-Aty3,4, Asoke Kumar Bhunia1
1 Department of Mathematics, The University of Burdwan, Burdwan, 713104, India
2 Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia
3 Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha, 61922, Saudi Arabia
4 Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt
* Corresponding Author: Ali Akbar Shaikh. Email:

Computer Systems Science and Engineering 2021, 38(3), 351-364. https://doi.org/10.32604/csse.2021.015451

Received 22 November 2020; Accepted 17 February 2021; Issue published 19 May 2021

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.

Keywords

Convexity of interval valued function; extended Fritz-John theorem; Interval order relation; Karlin’s constraint; saddle point optimality

Cite This Article

M. Sadikur Rahman, E. E. Mahmoud, A. Akbar Shaikh, A. Abdel-Aty and A. Kumar Bhunia, "Saddle point optimality criteria of interval valued non-linear programming problem," Computer Systems Science and Engineering, vol. 38, no.3, pp. 351–364, 2021.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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