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A new algorithm for concave quadratic programming

  • Moslem ZamaniEmail author
Article
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Abstract

The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a modified version by restricting the feasible set. This leads to a new bound for quadratic programs. We demonstrate that the dual of the bound is a semi-definite relaxation of quadratic programs. In addition, we probe the relationship between this bound and the well-known bounds in the literature. In the second part, thanks to the new bound, we propose a branch and cut algorithm for concave quadratic programs. We establish that the algorithm enjoys global convergence. The effectiveness of the method is illustrated for numerical problem instances.

Keywords

Non-convex quadratic programming Duality Semi-definite relaxation Bound Branch and cut method Concave quadratic programming 

Notes

Acknowledgements

I am very grateful to two anonymous referees for their valuable comments and suggestions which help to improve the paper considerably. The author would like to thank associate editor for the very thoughtful comments provided on the first version of this manuscript. This research was in part supported by a grant from the Iran National Science Foundation (No. 96010653, Principal investigator: Dr. Majid Soleimani-damaneh).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Parametric MultiObjective Optimization Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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