Volume 11, Issue 2 (9-2025)
mmr 2025, 11(2): 59-74 |
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Ghorbani-Moghadam K, Ghanbari R, Mohammadnia J. A pivoting algorithm for linear programming with linear complementarity constraints. mmr 2025; 11 (2) :59-74
URL: http://mmr.khu.ac.ir/article-1-3404-en.html
URL: http://mmr.khu.ac.ir/article-1-3404-en.html
1- Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran , k.ghorbani@khu.ac.ir
2- Ferdowsi University of Mashhad
2- Ferdowsi University of Mashhad
Abstract: (47 Views)
Linear programming problems with complementary linear constraints (LPCC) are widely studied in operations research and are known to be NP-hard. This paper explores a specific case of LPCC where the product of two variables must be zero, i.e., xp xm=0. This scenario frequently arises in optimization problems, particularly those involving absolute values that cannot be expressed as linear or integer programming problems. To tackle this, we will present a branch-and-bound algorithm, and we will implement the algorithm on numerical examples and compare its performance with existing methods.
Keywords: Linear Programming Problems, Linear Complementarity Constraints, Zero-one constraint, Branch and Bound Algorithm
Type of Study: Original Manuscript |
Subject:
Mat
Received: 2024/08/8 | Revised: 2025/11/8 | Accepted: 2025/07/30 | Published: 2025/09/6 | ePublished: 2025/09/6
Received: 2024/08/8 | Revised: 2025/11/8 | Accepted: 2025/07/30 | Published: 2025/09/6 | ePublished: 2025/09/6
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