Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

Jiawei Chen; Suliman Al-Homidan; Qamrul Hasan Ansari; Jun Li; Yibing Lv

doi:10.1007/s10957-021-01829-8

Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

J Optim Theory Appl. 2021;189(1):221-243. doi: 10.1007/s10957-021-01829-8. Epub 2021 Mar 2.

Authors

Jiawei Chen¹, Suliman Al-Homidan², Qamrul Hasan Ansari^{2

3}, Jun Li¹, Yibing Lv⁴

Affiliations

¹ School of Mathematics and Statistics, Southwest University, Chongqing, 400715 China.
² Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
³ Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002 India.
⁴ School of Information and Mathematics, Yangtze University, Jingzhou, 434023 China.

Abstract

In this paper, we study robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data. A robust counterpart of uncertain complex fractional programming is introduced in the worst-case scenario. The concept of robust optimal solution of the uncertain complex fractional programming is introduced by using robust counterpart. We give an equivalence between the optimal solutions of the robust counterpart and a minimax nonfractional parametric programming. Finally, Fritz John-type and Karush-Kuhn-Tucker-type robust necessary optimality conditions of the uncertain complex fractional programming are established under some suitable conditions.

Keywords: Robust constraint qualification; Robust counterpart; Robust necessary optimality conditions; Uncertain complex fractional programming.