Academic Journal
The Dual Simplex Method for Solving Bounded-Variable Linear Programs
| Title: | The Dual Simplex Method for Solving Bounded-Variable Linear Programs |
|---|---|
| Authors: | DJELOUD, Khalil |
| Source: | Statistics, Optimization & Information Computing; Vol. 16 No. 3 (2026); 2509-2525 ; 2310-5070 ; 2311-004X |
| Publisher Information: | International Academic Press |
| Publication Year: | 2026 |
| Collection: | International Academic Press (IAPress) |
| Subject Terms: | linear programming, long step rule, numerical experiments, open-source solver GLPK, dual simplex method |
| Description: | In this paper, we {propose a novel and robust} dual simplex algorithm for solving bounded-variable linear programming based on a structured dual support framework and an enhanced long-step rule. The method enables stable and efficient updates of both the support and the associated co-solution. Its effectiveness is supported by a rigorous theoretical analysis: we prove a sign-preservation property of the support co-solutions and derive an explicit expression for the variation of the objective function, ensuring controlled and monotonic improvement and yielding strong convergence guarantees. Extensive experiments on NETLIB problems benchmarks demonstrate that the proposed approach is competitive with the dual simplex implementation of GLPK, confirming its efficiency and reliability. |
| Document Type: | article in journal/newspaper |
| File Description: | application/pdf |
| Language: | English |
| Relation: | https://iapress.org/index.php/soic/article/view/3489/2038; https://iapress.org/index.php/soic/article/view/3489 |
| Availability: | https://iapress.org/index.php/soic/article/view/3489 |
| Rights: | Copyright (c) 2026 Khalil DJELOUD ; https://creativecommons.org/licenses/by/4.0 |
| Accession Number: | edsbas.17DD91F7 |
| Database: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://iapress.org/index.php/soic/article/view/3489# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: linear programming Type: general – SubjectFull: long step rule Type: general – SubjectFull: numerical experiments Type: general – SubjectFull: open-source solver GLPK Type: general – SubjectFull: dual simplex method Type: general Titles: – TitleFull: The Dual Simplex Method for Solving Bounded-Variable Linear Programs Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: DJELOUD, Khalil IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2026 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa Titles: – TitleFull: Statistics, Optimization & Information Computing; Vol. 16 No. 3 (2026); 2509-2525 ; 2310-5070 ; 2311-004X Type: main |
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