Featured Review:; The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems

Abstract

SIAM Review, Volume 67, Issue 4, Page 905-909, December 2025.
Optimal control theory has long been a cornerstone of mathematical modeling and decision-making across disciplines such as engineering, economics, and the physical sciences. Yet, as the complexity of control systems continues to grow, so does the demand for more robust and efficient computational techniques to solve these problems. Alfio Borzì’s The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems addresses this challenge head-on, introducing a groundbreaking numerical optimization procedure, the sequential quadratic Hamiltonian (SQH) method. This book not only builds upon the theoretical framework established by the Pontryagin maximum principle (PMP), but also offers a practical computational tool that is both versatile and robust. With applications ranging from differential Nash games to deep learning via residual neural networks, the book is as much a testament to the SQH method’s adaptability as it is to its computational power. In this review, we describe the book’s structure, its significant contributions to the field of applied and computational mathematics, and its interdisciplinary relevance. We explore how the SQH method redefines the landscape of optimal control, offering new pathways for both theoretical investigation and practical implementation.