Gustav Feichtinger – författare

At the 15th Viennese Workshop on Optimal Control and Dynamic Games, held in July 2022, experts in economics and the management sciences identified a concerning trend: static decision-making models, while less effective than dynamic ones, are becoming increasingly prevalent. This book aims to address the economic and social costs associated with reliance on static models and to demonstrate the advantages of applying dynamic approaches.

Static models may be easier to formulate, but they often overlook the long-term consequences of decisions, promoting myopic practices that can lead to poor outcomes. In contrast, dynamic models foster a more comprehensive perspective, enabling foresight in decision-making – which is crucial for issues involving stock variables, such as pollution, reputation, and inventory. The book explores the limitations of static models, including their inability to capture long-term outcomes, history-dependent solutions, and the impact of abrupt contextual changes. It also highlights recent advances in dynamic modeling techniques that can enhance accuracy and help adapt to complex decision-making environments.

By promoting the shift from static to dynamic models, this book aspires to open new research opportunities and provide valuable insights for researchers, students, policymakers, and managers in the fields of economics and the management sciences.

Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity.         

The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

Dynamic optimization is rocket science – and more. This volume teaches how to harness the modern theory of dynamic optimization to solve practical problems, not only from space flight but also in emerging social applications such as the control of drugs, corruption, and terror. These innovative domains are usefully thought about in terms of populations, incentives, and interventions, concepts which map well into the framework of optimal dynamic control. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. We celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding – and push its frontiers by exploring models that display multiple equilibria whose basins of attraction are separated by higher-dimensional DNSS "tipping points". That rich theory is complemented by numerical methods available through a companion web site.