Alternating Direction Method of Multipliers (ADMM) Techniques for Embedded Mixed-Integer Quadratic Programming and Applications

Abstract

In this project, we delve into an important class of constrained nonconvex problems known as mixed-integer quadratic programming (MIQP). The popularity of MIQP is primarily due to the fact that many real-world problems can be described via MIQP models. The development of efficient MIQP algorithms has been an active and rapidly evolving field of research. As a matter of fact, previously well-known techniques for MIQP problems are found unsuitable for large-scale or online MIQP problems where algorithm’s computational efficiency is a crucial factor. In this regard, the alternating direction method of multipliers (ADMM) as a heuristic has shown to offer satisfactory suboptimal solutions with much improved computational complexity relative to global solvers based on for example branch-and-bound. This project provides the necessary details required to understand the ADMM-based algorithms as applied to MIQP problems. Three illustrative examples are also included in this project to demonstrate the effectiveness of the ADMM algorithm through numerical simulations and performance comparisons.