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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Vydané v:	Journal of optimization theory and applications Ročník 177; číslo 3; s. 835 - 856
Hlavní autori:	Wei, Hong-Zhi, Chen, Chun-Rong, Li, Sheng-Jie
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.06.2018 Springer Nature B.V
Predmet:	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
Author_xml	– sequence: 1 givenname: Hong-Zhi surname: Wei fullname: Wei, Hong-Zhi organization: College of Mathematics and Statistics, Chongqing University – sequence: 2 givenname: Chun-Rong orcidid: 0000-0001-8285-7881 surname: Chen fullname: Chen, Chun-Rong email: chencr1981@163.com organization: College of Mathematics and Statistics, Chongqing University – sequence: 3 givenname: Sheng-Jie surname: Li fullname: Li, Sheng-Jie organization: College of Mathematics and Statistics, Chongqing University
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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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