Optimality Conditions and Image Space Analysis for Vector Optimization Problems

2011 ◽  
pp. 169-220 ◽  
Author(s):  
Giandomenico Mastroeni
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Image Space Analysis ◽  
Image Space ◽  
Vector Optimization Problems ◽  
Space Analysis

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>

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

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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