An Exact Algorithm Based on the Kuhn–Tucker Conditions for Solving Linear Generalized Semi-Infinite Programming Problems
Optimization problems containing a finite number of variables and an infinite number of constraints are called semi-infinite programming problems. Under certain conditions, a class of these problems can be represented as bi-level programming problems. Bi-level problems are a particular class of opti...
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          | Published in | Journal of mathematics (Hidawi) Vol. 2022; no. 1 | 
|---|---|
| Main Authors | , | 
| Format | Journal Article | 
| Language | English | 
| Published | 
        Cairo
          Hindawi
    
        2022
     John Wiley & Sons, Inc Wiley  | 
| Subjects | |
| Online Access | Get full text | 
| ISSN | 2314-4629 2314-4785 2314-4785  | 
| DOI | 10.1155/2022/1765385 | 
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| Abstract | Optimization problems containing a finite number of variables and an infinite number of constraints are called semi-infinite programming problems. Under certain conditions, a class of these problems can be represented as bi-level programming problems. Bi-level problems are a particular class of optimization problems, in which there is another optimization problem embedded in one of the constraints. We reformulate a semi-infinite problem into a bi-level problem and then into a single-level nonlinear one by using the Kuhn–Tucker optimality conditions. The resulting reformulation allows us to employ a branch and bound scheme to optimally solve the problem. Computational experimentation over well-known instances shows the effectiveness of the developed method concluding that it is able to effectively solve linear semi-infinite programming problems. Additionally, some linear bi-level problems from literature are used to validate the robustness of the proposed algorithm. | 
    
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| AbstractList | Optimization problems containing a finite number of variables and an infinite number of constraints are called semi-infinite programming problems. Under certain conditions, a class of these problems can be represented as bi-level programming problems. Bi-level problems are a particular class of optimization problems, in which there is another optimization problem embedded in one of the constraints. We reformulate a semi-infinite problem into a bi-level problem and then into a single-level nonlinear one by using the Kuhn–Tucker optimality conditions. The resulting reformulation allows us to employ a branch and bound scheme to optimally solve the problem. Computational experimentation over well-known instances shows the effectiveness of the developed method concluding that it is able to effectively solve linear semi-infinite programming problems. Additionally, some linear bi-level problems from literature are used to validate the robustness of the proposed algorithm. | 
    
| Author | Camacho-Vallejo, José-Fernando Barragán, Abraham  | 
    
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| Cites_doi | 10.1007/978-1-4419-9164-5 10.1109/tevc.2017.2712906 10.3390/mol2net-04-05881 10.1016/j.ejco.2021.100006 10.1007/s12559-018-9561-1 10.1016/j.ejor.2012.06.009 10.1016/s0377-2217(99)00132-0 10.1007/978-1-4757-2836-1 10.1016/j.ejor.2007.01.057 10.1016/s0377-2217(01)00307-1 10.1137/1035089 10.13053/cys-22-2-2943 10.1016/j.orl.2020.02.007 10.1007/978-1-4757-2868-2_7 10.1007/s10957-010-9674-5 10.1007/s10589-012-9489-4 10.1155/2016/4360909 10.1016/j.cam.2007.02.012 10.1016/j.apm.2011.02.008 10.1016/j.ejor.2019.10.025  | 
    
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| Copyright | Copyright © 2022 Abraham Barragán and José-Fernando Camacho-Vallejo. Copyright © 2022 Abraham Barragán and José-Fernando Camacho-Vallejo. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0  | 
    
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| References | Barragán A. B (e_1_2_9_15_2) 2018; 22 Hoffmann A. (e_1_2_9_17_2) 1994 Dempe S. (e_1_2_9_22_2) 2002 Barragán A. B. (e_1_2_9_14_2) 2018; 27 Barragán A. B. (e_1_2_9_12_2) 2016; 69 e_1_2_9_13_2 e_1_2_9_18_2 e_1_2_9_19_2 Goberna M. A. (e_1_2_9_10_2) 1998 Hettich R. (e_1_2_9_16_2) 1991 e_1_2_9_21_2 e_1_2_9_20_2 e_1_2_9_23_2 e_1_2_9_7_2 e_1_2_9_6_2 e_1_2_9_5_2 e_1_2_9_4_2 e_1_2_9_3_2 e_1_2_9_2_2 e_1_2_9_1_2 Leal-Coronado M. A. (e_1_2_9_26_2) 2016; 7 e_1_2_9_9_2 e_1_2_9_8_2 e_1_2_9_25_2 Polak E. (e_1_2_9_11_2) 1997 e_1_2_9_24_2 e_1_2_9_27_2 e_1_2_9_28_2  | 
    
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| Snippet | Optimization problems containing a finite number of variables and an infinite number of constraints are called semi-infinite programming problems. Under... Optimization problems containing a finite number of variables and an infinite number of constraints are called semi‐infinite programming problems. Under...  | 
    
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| SubjectTerms | Algorithms Experimentation Kuhn-Tucker method Mathematics Methods Optimization Programming Reproducibility  | 
    
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| Title | An Exact Algorithm Based on the Kuhn–Tucker Conditions for Solving Linear Generalized Semi-Infinite Programming Problems | 
    
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