Multi-start approach for an integer determinant maximization problem

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.