scholarly journals Numerical method for solving the continuous-time linear programming problems with time-dependent matrices and piecewise continuous functions

2020 ◽  
Vol 5 (6) ◽  
pp. 5571-5626
Author(s):  
Hsien-Chung Wu ◽  
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Continuous Time ◽  
Continuous Functions ◽  
Time Dependent ◽  
Linear Programming Problems ◽  
Piecewise Continuous ◽  
Time Linear

scholarly journals Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 435
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Linear Programming ◽  
Robust Optimization ◽  
Numerical Method ◽  
Programming Problem ◽  
Continuous Time ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Robust Counterpart ◽  
Linear Programming Problems ◽  
Time Linear

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.

scholarly journals Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 885
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Continuous Time ◽  
Linear Programming Problem ◽  
Computational Procedure ◽  
Time Dependent ◽  
Optimal Solutions ◽  
Robust Counterpart ◽  
Linear Programming Problems ◽  
Time Linear

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.

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