A Simplex Algorithm for the Local Minimization of a Box-Constrained Concave Quadratic Program

In this work, we extend the simplex algorithm of linear programming for finding a local minimum of a concave quadratic function subject to box constraints. In order to test the performance of the proposed algorithm, we have developed an implementation with MATLAB. The simplex algorithm is tested on...

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Bibliographic Details
Published in:2024 International Conference of the African Federation of Operational Research Societies (AFROS) pp. 1 - 6
Main Authors: Bentobache, Mohand, Telli, Mohamed, Mokhtari, Abdelkader
Format: Conference Proceeding
Language:English
Published: IEEE 03.11.2024
Subjects:
Algorithms
Box-constrained concave quadratic programming
Computer languages
Libraries
Linear programming
Local minimum
Mathematical models
MATLAB
Minimization
Numerical experiments
Optimization
Physics
Quadratic programming
Simplex algorithm
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Summary:In this work, we extend the simplex algorithm of linear programming for finding a local minimum of a concave quadratic function subject to box constraints. In order to test the performance of the proposed algorithm, we have developed an implementation with MATLAB. The simplex algorithm is tested on a set of 5 box-constrained QP test instances corresponding to a mathematical model arising a statistical physics application and 48 test problems taken from the CUTEr library. The obtained numerical results are very encouraging. Indeed, the local minimizer obtained with the simplex algorithm is global for the majority of the considered test problems.
DOI:10.1109/AFROS62115.2024.11037212