A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems

2019 ◽  
Vol 184 (2) ◽  
pp. 466-493 ◽  
Author(s):  
Hong-Zhi Wei ◽  
Chun-Rong Chen ◽  
Sheng-Jie Li
Keyword(s):  
Optimization Problems ◽  
Image Space Analysis ◽  
Image Space ◽  
Unified Approach ◽  
Space Analysis ◽  
Uncertain Optimization

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiaoqing Ou ◽  
Suliman Al-Homidan ◽  
Qamrul Hasan Ansari ◽  
Jiawei Chen
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Image Space Analysis ◽  
Image Space ◽  
Inclusion Problems ◽  
Space Analysis ◽  
Multiobjective Optimization Problems ◽  
Weak Separation

<p style='text-indent:20px;'>We introduce the <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution and optimistic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution of uncertain multiobjective optimization problems (UMOP). By using image space analysis, robust optimality conditions as well as saddle point sufficient optimality conditions for uncertain multiobjective optimization problems are established based on real-valued linear (regular) weak separation function and real-valued (vector-valued) nonlinear (regular) weak separation functions. We also introduce two inclusion problems by using the image sets of robust counterpart of (UMOP) and establish the relations between the solution of the inclusion problems and the <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution (respectively, optimistic <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{C} $\end{document}</tex-math></inline-formula>-robust efficient solution) of (UMOP).</p>

Characterizations of robust optimality conditions via image space analysis

Optimization ◽  
2020 ◽  
Vol 69 (9) ◽  
pp. 2063-2083
Author(s):  
Q. H. Ansari ◽  
P. K. Sharma ◽  
X. Qin
Keyword(s):  
Optimality Conditions ◽  
Image Space Analysis ◽  
Image Space ◽  
Space Analysis
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