Characterizations for Optimality Conditions of General Robust Optimization Problems

Hong-Zhi Wei (), Chun-Rong Chen () and Sheng-Jie Li ()
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Hong-Zhi Wei: Chongqing University
Chun-Rong Chen: Chongqing University
Sheng-Jie Li: Chongqing University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 14, 835-856

Abstract: 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.

Keywords: Image space analysis; Scalar robust optimization; Corrected image; Robust optimality condition; 90C31; 90C30; 90C46 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10957-018-1256-y

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