# Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

## TL;DR

This paper introduces a new decomposition method combining penalty-based Lagrangian and Gauss-Seidel techniques to efficiently solve stochastic mixed-integer programming problems, demonstrating superior computational performance and solution quality.

## Contribution

The paper presents a novel PBGS approach that leverages problem structure for improved efficiency over existing methods like Progressive Hedging.

## Key findings

- PBGS outperforms PH in computational speed
- PBGS achieves higher solution quality
- Numerical experiments validate efficiency and effectiveness

## Abstract

In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of the proposed method is compared with the Progressive Hedging method (PH), which also can be viewed as a Lagrangian-based method for obtaining solutions for SMIP. Numerical experiments performed using instances from the literature illustrate the efficiency of the proposed method in terms of computational performance and solution quality.