American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021199
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

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

Received  April 2021 Revised  August 2021 Early access November 2021

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).

Citation: Xiaoqing Ou, Suliman Al-Homidan, Qamrul Hasan Ansari, Jiawei Chen. Image space analysis for uncertain multiobjective optimization problems: Robust optimality conditions. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021199
References:

show all references

References:
 [1] Hong-Zhi Wei, Chun-Rong Chen. Three concepts of robust efficiency for uncertain multiobjective optimization problems via set order relations. Journal of Industrial & Management Optimization, 2019, 15 (2) : 705-721. doi: 10.3934/jimo.2018066 [2] Jiawei Chen, Shengjie Li, Jen-Chih Yao. Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points. Journal of Industrial & Management Optimization, 2020, 16 (2) : 707-724. doi: 10.3934/jimo.2018174 [3] Jutamas Kerdkaew, Rabian Wangkeeree, Rattanaporn Wangkeeree. Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators. Numerical Algebra, Control & Optimization, 2022, 12 (1) : 93-107. doi: 10.3934/naco.2021053 [4] Fengming Lin, Xiaolei Fang, Zheming Gao. Distributionally Robust Optimization: A review on theory and applications. Numerical Algebra, Control & Optimization, 2022, 12 (1) : 159-212. doi: 10.3934/naco.2021057 [5] Gaoxi Li, Zhongping Wan, Jia-wei Chen, Xiaoke Zhao. Necessary optimality condition for trilevel optimization problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 55-70. doi: 10.3934/jimo.2018140 [6] Ruotian Gao, Wenxun Xing. Robust sensitivity analysis for linear programming with ellipsoidal perturbation. Journal of Industrial & Management Optimization, 2020, 16 (4) : 2029-2044. doi: 10.3934/jimo.2019041 [7] Matthew H. Henry, Yacov Y. Haimes. Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty. Journal of Industrial & Management Optimization, 2009, 5 (4) : 791-824. doi: 10.3934/jimo.2009.5.791 [8] Jutamas Kerdkaew, Rabian Wangkeeree. Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2651-2673. doi: 10.3934/jimo.2019074 [9] Xiang-Kai Sun, Xian-Jun Long, Hong-Yong Fu, Xiao-Bing Li. Some characterizations of robust optimal solutions for uncertain fractional optimization and applications. Journal of Industrial & Management Optimization, 2017, 13 (2) : 803-824. doi: 10.3934/jimo.2016047 [10] Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 [11] Lingshuang Kong, Changjun Yu, Kok Lay Teo, Chunhua Yang. Robust real-time optimization for blending operation of alumina production. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1149-1167. doi: 10.3934/jimo.2016066 [12] Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 [13] Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest, Stefan W. Pickl. A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure. Journal of Industrial & Management Optimization, 2021, 17 (2) : 669-686. doi: 10.3934/jimo.2019128 [14] Nazih Abderrazzak Gadhi, Fatima Zahra Rahou. Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021216 [15] Ningyu Sha, Lei Shi, Ming Yan. Fast algorithms for robust principal component analysis with an upper bound on the rank. Inverse Problems & Imaging, 2021, 15 (1) : 109-128. doi: 10.3934/ipi.2020067 [16] Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu. Strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems & Imaging, 2012, 6 (2) : 357-372. doi: 10.3934/ipi.2012.6.357 [17] G. Mastroeni, L. Pellegrini. On the image space analysis for vector variational inequalities. Journal of Industrial & Management Optimization, 2005, 1 (1) : 123-132. doi: 10.3934/jimo.2005.1.123 [18] Shouhong Yang. Semidefinite programming via image space analysis. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1187-1197. doi: 10.3934/jimo.2016.12.1187 [19] Alireza Goli, Hasan Khademi Zare, Reza Tavakkoli-Moghaddam, Ahmad Sadeghieh. Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 187-209. doi: 10.3934/naco.2019014 [20] Nithirat Sisarat, Rabian Wangkeeree, Gue Myung Lee. Some characterizations of robust solution sets for uncertain convex optimization problems with locally Lipschitz inequality constraints. Journal of Industrial & Management Optimization, 2020, 16 (1) : 469-493. doi: 10.3934/jimo.2018163

2020 Impact Factor: 1.801