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A successive linear approximation algorithm for the global minimization of a concave quadratic program

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Abstract

In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.

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Acknowledgements

The authors are indebted to the anonymous referees whose comments and suggestions have considerably improved the quality of this paper.

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Authors and Affiliations

  1. Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, BP 37G, Ghardaia Road, 03000, Laghouat, Algeria

    Mohamed Telli, Mohand Bentobache & Abdelkader Mokhtari

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  1. Mohamed Telli
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  2. Mohand Bentobache
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  3. Abdelkader Mokhtari
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Correspondence to Mohand Bentobache.

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Communicated by Ernesto G. Birgin.

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Telli, M., Bentobache, M. & Mokhtari, A. A successive linear approximation algorithm for the global minimization of a concave quadratic program. Comp. Appl. Math. 39, 272 (2020). https://doi.org/10.1007/s40314-020-01317-1

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