Using a conic bundle method to accelerate both phases of a quadratic convex reformulation
Abstract
We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem , and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm.
Cite
@article{arxiv.1603.00347,
title = {Using a conic bundle method to accelerate both phases of a quadratic convex reformulation},
author = {Alain Billionnet and Sourour Elloumi and Amélie Lambert and Angelika Wiegele},
journal= {arXiv preprint arXiv:1603.00347},
year = {2020}
}