Abstract
The uncertainty for the continuous-time linear programming problem with time-dependent matrices is considered in this paper. In this case, the robust counterpart of the continuous-time linear programming problem is introduced. In order to solve the robust counterpart, it will be transformed into the conventional form of the continuous-time linear programming problem with time-dependent matrices. The discretization problem is formulated for the sake of numerically calculating the ϵ-optimal solutions, and a computational procedure is also designed to achieve this purpose.
Highlights
The theory of the continuous-time linear programming problem originated from the “bottleneck problem” proposed by Bellman [1]
When the data in the continuous-time linear programming problem with time-dependent matrices are uncertain, a robust counterpart should be established and solved, which is the purpose of this paper
We introduce the concept of an -optimal solution to obtain the approximate solution
Summary
The theory of the continuous-time linear programming problem originated from the “bottleneck problem” proposed by Bellman [1]. A continuous-time linear programming problem with constant matrices was formulated and studied rigorously by Tyndall [2,3]. We study the time-dependent matrices that is more complicated than the constant matrices. Levinson [4] studied the problem of time-dependent matrices, the numerical methodology was not proposed to effectively calculate the optimal solution. Wu [5] tried to design a computational procedure to calculate the approximate optimal solutions. When the data in the continuous-time linear programming problem with time-dependent matrices are uncertain, a robust counterpart should be established and solved, which is the purpose of this paper
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