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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| Vydané v: | Mathematics (Basel) Ročník 7; číslo 5; s. 435 |
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01.05.2019
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| ISSN: | 2227-7390, 2227-7390 |
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| 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. |
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| AbstractList | 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. |
| Author | Wu, Hsien-Chung |
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| Cites_doi | 10.1016/0022-247X(66)90187-9 10.1007/s10107-005-0679-z 10.1137/0321046 10.1080/01630563.2016.1193517 10.1016/0022-247X(74)90124-3 10.1016/0022-247X(82)90163-9 10.1007/BF00934631 10.1007/s10107-005-0677-1 10.1007/s10898-011-9751-9 10.1007/s10898-010-9542-8 10.1016/0022-247X(80)90278-4 10.1007/s10107-005-0678-0 10.1080/01630563.2011.629312 10.1137/0115112 10.1007/BF01303432 10.1016/0022-247X(74)90280-7 10.1007/s10107-008-0217-x 10.1287/moor.23.4.769 10.1137/S1052623496305717 10.1137/S1052623494278827 10.1016/0022-247X(80)90230-9 10.1007/s10107-006-0710-z 10.1016/0022-247X(77)90072-5 10.1016/0022-247X(69)90106-1 10.1137/S0895479896298130 10.1006/jmaa.1997.5377 10.1287/opre.1030.0065 10.1287/mnsc.1.3-4.197 10.1016/0022-247X(72)90262-4 10.1137/S0363012992227216 10.1007/s10107-002-0307-0 10.1006/jmaa.1998.6024 10.1137/S0363012993247858 10.1016/S0167-6377(99)00016-4 10.1016/0022-247X(68)90184-4 10.1287/moor.1050.0166 10.1287/opre.1070.0441 10.1137/0113043 10.1007/s10957-007-9301-2 10.1007/s10957-006-9082-z 10.1137/S0363012993257507 10.1137/0331073 10.1007/s10957-007-9302-1 10.1137/060650003 10.1016/0022-247X(80)90149-3 10.1016/0022-247X(78)90143-9 10.1016/0022-247X(69)90143-7 10.1137/140971725 |
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| SubjectTerms | Algorithms approximate solutions continuous-time linear programming problems Linear programming Mathematical functions Numerical analysis Numerical methods Optimization robust optimization Robustness (mathematics) ϵ-optimal solutions |
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| Title | Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems |
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