Projective Cutting Planes for General QP with Indicator Constraints

General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous … Read more

An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problems

Cardinality-constrained optimization problems are notoriously hard to solve both in theory and practice. However, as famous examples such as the sparse portfolio optimization and best subset selection problems show, this class is extremely important in real-world applications. In this paper, we apply a penalty alternating direction method to these problems. The key idea is to … Read more

Exact solution of the donor-limited nearest neighbor hot deck imputation problem

Data quality in population surveys suffers from missing responses. We use combinatorial optimization to create a complete and coherent data set. The methods are based on the widespread nearest neighbor hot deck imputation method that replaces the missing values with observed values from a close unit, the so-called donor. As a repeated use of donors … Read more

A mixed-integer optimization approach to an exhaustive cross-validated model selection for regression

We consider a linear regression model for which we assume that many of the observed regressors are irrelevant for the prediction. To avoid overfitting, we conduct a variable selection and only include the true predictors for the least square fitting. The best subset selection gained much interest in recent years for addressing this objective. For … Read more