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

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 h...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 7; no. 5; p. 435
Main Author: Wu, Hsien-Chung
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2019
Subjects:
Algorithms
approximate solutions
continuous-time linear programming problems
Linear programming
Mathematical functions
Numerical analysis
Numerical methods
Optimization
robust optimization
Robustness (mathematics)
ϵ-optimal solutions
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math7050435