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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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 177; no. 3; pp. 835 - 856
Main Authors: Wei, Hong-Zhi, Chen, Chun-Rong, Li, Sheng-Jie
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2018
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1256-y