Multi-start approach for an integer determinant maximization problem

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.

Keywords:

• determinant maximization
• trust-region algorithm
• conic optimization
• multi-start framework

AMS Subject Classifications::

• 90C22
• 90C90

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.