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 inJournal of mathematics (Hidawi) Vol. 2022; no. 1
Main Authors Barragán, Abraham, Camacho-Vallejo, José-Fernando
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects
Online AccessGet full text
ISSN2314-4629
2314-4785
2314-4785
DOI10.1155/2022/1765385

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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.
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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ContentType Journal Article
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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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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