Image space analysis for uncertain multiobjective optimization problems: Robust optimality conditions

Xiaoqing Ou; Suliman Al-Homidan; Qamrul Hasan Ansari; Jiawei Chen

doi:10.3934/jimo.2021199

Article Contents

2023, Volume 19, Issue 1: 629-644. Doi: 10.3934/jimo.2021199

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Image space analysis for uncertain multiobjective optimization problems: Robust optimality conditions

1.
College of Management, Chongqing College of Humanities, Science & Technology, Chongqing 401524, China
2.
Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
3.
Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
4.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Corresponding author: Jiawei Chen
Corresponding author: Jiawei Chen

Received: April 2021

Revised: August 2021

Early access: November 2021

Published: January 2023

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Abstract

We introduce the $ \mathcal{C} $-robust efficient solution and optimistic $ \mathcal{C} $-robust efficient solution of uncertain multiobjective optimization problems (UMOP). By using image space analysis, robust optimality conditions as well as saddle point sufficient optimality conditions for uncertain multiobjective optimization problems are established based on real-valued linear (regular) weak separation function and real-valued (vector-valued) nonlinear (regular) weak separation functions. We also introduce two inclusion problems by using the image sets of robust counterpart of (UMOP) and establish the relations between the solution of the inclusion problems and the $ \mathcal{C} $-robust efficient solution (respectively, optimistic $ \mathcal{C} $-robust efficient solution) of (UMOP).

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Mathematics Subject Classification: Primary: 90C29, 90C46; Secondary: 49K45.

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