Active Set methods for solving large sample average approximations of chance constrained optimisation problems

TL;DR

This paper introduces an Active Set method for efficiently solving large sample average approximation problems in chance-constrained programming, demonstrating improved scalability and performance over existing methods.

Contribution

The paper presents a novel Active Set approach that significantly enhances the solution speed for large-scale chance-constrained problems, especially with many scenarios.

Findings

Active Set method solves large SAA problems quickly

Increasing scenarios improves solution quality more than small-scenario accuracy

Method extends effectively to integer programming models

Abstract

This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which improves on some existing methods. Our Active Set method allows one to solve SAAs of chance-constrained programs with very large numbers of scenarios quickly. We demonstrate that increasing the number of scenarios is more important than improving accuracy with small numbers of scenarios. We use an example of the portfolio selection problem to demonstrate the relative performance of previous and new methods. Extending the Active Set method to an integer-programming model further highlights its applicability and further improves over previous approaches.