Characterizations for Optimality Conditions of General Robust Optimization Problems

In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered, among which, the uncertainties are included in the objective as well as the constraints. Besides, on the strength of a corrected image in a new...

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Vydáno v:Journal of optimization theory and applications Ročník 177; číslo 3; s. 835 - 856
Hlavní autoři: Wei, Hong-Zhi, Chen, Chun-Rong, Li, Sheng-Jie
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2018
Springer Nature B.V
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Nonlinear programming
Operations Research/Decision Theory
Optimization
Robustness
Saddle points
Shortest-path problems
Theory of Computation
90C31
90C30
90C46
Robust optimality condition
Image space analysis
Scalar robust optimization
Corrected image
ISSN:0022-3239, 1573-2878
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Abstract In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered, among which, the uncertainties are included in the objective as well as the constraints. Besides, on the strength of a corrected image in a new type, an equivalent relation between the uncertain optimization problem and its image problem is also established, which provides an idea to tackle with minimax problems. Furthermore, theorems of the robust weak alternative as well as sufficient characterizations of robust optimality conditions are achieved on the frame of the linear and nonlinear (regular) weak separation functions. Moreover, several necessary and sufficient optimality conditions, especially saddle point sufficient optimality conditions for scalar robust optimization problems, are obtained. Finally, a simple example for finding a shortest path is included to show the effectiveness of the results derived in this paper.
AbstractList In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered, among which, the uncertainties are included in the objective as well as the constraints. Besides, on the strength of a corrected image in a new type, an equivalent relation between the uncertain optimization problem and its image problem is also established, which provides an idea to tackle with minimax problems. Furthermore, theorems of the robust weak alternative as well as sufficient characterizations of robust optimality conditions are achieved on the frame of the linear and nonlinear (regular) weak separation functions. Moreover, several necessary and sufficient optimality conditions, especially saddle point sufficient optimality conditions for scalar robust optimization problems, are obtained. Finally, a simple example for finding a shortest path is included to show the effectiveness of the results derived in this paper.
Author Li, Sheng-Jie
Wei, Hong-Zhi
Chen, Chun-Rong
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  surname: Chen
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  organization: College of Mathematics and Statistics, Chongqing University
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  surname: Li
  fullname: Li, Sheng-Jie
  organization: College of Mathematics and Statistics, Chongqing University
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Keywords 90C31
90C30
90C46
Robust optimality condition
Image space analysis
Scalar robust optimization
Corrected image
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Snippet In this paper, by virtue of the image space analysis, the general scalar robust optimization problems under the strictly robust counterpart are considered,...
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SubjectTerms Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Nonlinear programming
Operations Research/Decision Theory
Optimization
Robustness
Saddle points
Shortest-path problems
Theory of Computation
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Title Characterizations for Optimality Conditions of General Robust Optimization Problems
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