Abstract
In this article, we present a multi-start approach to solve a determinant maximization problem of an integer matrix variable that has a constant trace. In order to enforce that elements of the matrix variable are integer, we add a nonlinear repeller term to the objective function. To solve this nonlinear optimization problem we implement our sequential conic trust-region-based algorithm within a multi-start framework. To demonstrate the potential of our approach, we use a determinant maximization model from crystallography.
Acknowledgements
We thank two anonymous referees for their constructive comments and suggestions to improve an earlier versions of this article. The second author was partially supported by a start-up package of Lehigh University, The Canada Research Chair Program and NSERC.