Real-time solution of quadratic optimization problems with banded matrices and indicator variables

TL;DR

This paper introduces a real-time method for solving mixed-integer quadratic optimization problems with banded matrices and indicator variables, leveraging decision diagrams for efficient online solutions in statistical and monitoring applications.

Contribution

It presents a novel approach using decision diagrams to efficiently solve these problems in milliseconds, exploiting temporal dependencies for polynomial-sized diagrams.

Findings

Decision diagrams enable polynomial-sized representations.

The method achieves millisecond solution times.

Applicable to real-time monitoring and anomaly detection.

Abstract

We consider mixed-integer quadratic optimization problems with banded matrices and indicator variables. These problems arise pervasively in statistical inference problems with time-series data, where the banded matrix captures the temporal relationship of the underlying process. In particular, the problem studied arises in monitoring problems, where the decision-maker wants to detect changes or anomalies. We propose to solve these problems using decision diagrams. In particular we show how to exploit the temporal dependencies to construct diagrams with size polynomial in the number of decision variables. We also describe how to construct the convex hull of the set under study from the decision diagrams, and how to deploy the method online to solve the problems in milliseconds via a shortest path algorithm.