The Dual Simplex Method for Solving Bounded-Variable Linear Programs
DOI:
https://doi.org/10.19139/soic-2310-5070-3489Keywords:
linear programming, long step rule, numerical experiments, open-source solver GLPK, dual simplex method.Abstract
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.Downloads
Published
2026-07-17
How to Cite
DJELOUD, K. (2026). The Dual Simplex Method for Solving Bounded-Variable Linear Programs. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3489
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Section
Research Articles
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Copyright (c) 2026 Khalil DJELOUD
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