Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices
An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/5/211 |
| _version_ | 1827670375364820992 |
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| author | Hsien-Chung Wu |
| author_facet | Hsien-Chung Wu |
| author_sort | Hsien-Chung Wu |
| collection | DOAJ |
| description | An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared in the problem are considered to be uncertain quantities, which are treated according to the concept of robust optimization. A discretization problem of the robust counterpart is formulated and solved to obtain the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-optimal solutions. |
| first_indexed | 2024-03-10T03:20:09Z |
| format | Article |
| id | doaj.art-296e602007a242c595884c8f67fed9cf |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T03:20:09Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-296e602007a242c595884c8f67fed9cf2023-11-23T10:04:09ZengMDPI AGAxioms2075-16802022-05-0111521110.3390/axioms11050211Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent MatricesHsien-Chung Wu0Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, TaiwanAn extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared in the problem are considered to be uncertain quantities, which are treated according to the concept of robust optimization. A discretization problem of the robust counterpart is formulated and solved to obtain the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-optimal solutions.https://www.mdpi.com/2075-1680/11/5/211approximate solutionscontinuous-time linear programming problemsϵ-optimal solutionsrobust optimizationweak duality |
| spellingShingle | Hsien-Chung Wu Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices Axioms approximate solutions continuous-time linear programming problems ϵ-optimal solutions robust optimization weak duality |
| title | Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices |
| title_full | Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices |
| title_fullStr | Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices |
| title_full_unstemmed | Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices |
| title_short | Extended Form of Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices |
| title_sort | extended form of robust solutions for uncertain continuous time linear programming problems with time dependent matrices |
| topic | approximate solutions continuous-time linear programming problems ϵ-optimal solutions robust optimization weak duality |
| url | https://www.mdpi.com/2075-1680/11/5/211 |
| work_keys_str_mv | AT hsienchungwu extendedformofrobustsolutionsforuncertaincontinuoustimelinearprogrammingproblemswithtimedependentmatrices |