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In this paper, by means of linear and nonlinear (regular) weak separation functions, we obtain some characterizations of robust optimality conditions for uncertain optimization problems, especially saddle point sufficient optimality conditions. Additionally, the relationships between three approaches used for robustness analysis: image space analysis, vector optimization and set-valued optimization, are discussed. Finally, an application for finding a shortest path is given to verify the validity of the results derived in this paper. [ABSTRACT FROM AUTHOR]

In this paper, by virtue of the image space analysis, we investigate general scalar robust optimization problems with uncertainties both in the objective and constraints. Under mild assumptions, we characterize various robust solutions for different kinds of robustness concepts, by introducing suitable images of the original uncertain problem, or the images of its counterpart problems appropriately, which provide a unified approach to tackling with robustness for uncertain optimization problems. Several examples are employed to show the effectiveness of the results derived in this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization results for several set order relations, together with the help of image space analysis, some suitable subsets of scalarization image space are introduced to make equivalent characterizations for upper set (lower set, set, certainly, respectively) less ordered robustness for uncertain multiobjective optimization problems. In particular, the nonlinear scalarization functional plays a significant role in computing various multiobjective robust solutions. Finally, the corresponding examples are included to show the effectiveness of the results derived in this paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]