A new dual for quadratic programming and its applications
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 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.
Cite
@article{arxiv.1808.01266,
title = {A new dual for quadratic programming and its applications},
author = {Moslem Zamani},
journal= {arXiv preprint arXiv:1808.01266},
year = {2019}
}