Abstract
A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which has been extensively studied recently. We introduce the robust counterpart of the continuous-time linear programming problem. In order to solve this robust counterpart, a discretization problem is formulated and solved to obtain the ϵ -optimal solution. The important contribution of this paper is to locate the error bound between the optimal solution and ϵ -optimal solution.
Highlights
The theory of continuous-time linear programming problem has received considerable attention for a long time
Based on the solutions obtained from the discretization problem, we can construct the feasible solutions of the transformed problem
The continuous-time linear programming problem with uncertain data has been studied in this paper
Summary
The theory of continuous-time linear programming problem has received considerable attention for a long time. We are going to consider the continuous-time linear programming problem in which the data are assumed to be uncertain. We shall solve a more general model that considers the uncertain data in continuous-time linear programming problem. In order to address the optimization problems with uncertain data falling into the uncertainty sets, Ben-Tal and Nemirovski [41,42] and independently El Ghaoui [43,44] proposed to solve the so-called robust optimization problems. This topic has increasingly received much attention.
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