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.
Spis treści
Part I Mathematical Methods.-On Some Open Problems in Optimal Control.-On Nonlocal Normal Forms of Linear Second Order Mixed Type PDEs on the Plane.-Discrete Filippov-Type Stability for One-Sided Lipschitzian Dierence Inclusions.-Solution Stability and Path-Following for a Class of Generalized Equations.-On the Dynamic Programming Approach to Incentive Constraint Problems.-A Functional Analytic Approach to a Bolza Problem.-On the Generalized Duality Principle for State-Constrained Control and State Estimation Under Impulsive Inputs.-Positive Approximations of the Inverse of Fractional Powers of SPD M-Matrices.-A General Lagrange Multipliers Theorem and Related Questions.-Strict Dissipativity Implies Turnpike Behavior for Time Varying Discrete Time Optimal Control Problems.-Part II Economics and Environmental Models.-Optimal Exploitation of Renewable Resources: Lessons in Sustainability from an Optimal Growth Model of Natural Resource Consumption.-(LNG) Arbitrage, Intertemporal Market Equilibrium and (Political) Uncertainty.-The Deterministic Optimal Liquidation Problem.-Dynamic Models of the Firm with Green Energy and Goodwill.-An Extended Integrated Assessment Model for Mitigation & Adaptation Policies on Climate Change.-Part III Population Dynamics and Spatial Models.-Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case.-Does Demography Change Wealth Inequality?-Stability Analysis of a New E-Rumor Model.-Optimal Spatiotemporal Management of Resources and Economic Activities Under Pollution Externalities.-Some Regional Control Problems for Population Dynamics.
O autorze
Gustav Feichtinger is a Professor Emeritus of Operations Research at the Vienna University of Technology (TU Wien). Moreover, he is Research Group Leader for Population Economics at the Vienna Institute of Demography of the Austrian Academy of Sciences. He is a Corresponding Member of the academy and holds an Honorary Doctorate from the Otto von Guericke University of Magdeburg. His main interests are in the economic applications of optimal control theory, dynamic games and nonlinear dynamical systems, as well as population mathematics.
Raimund Kovacevic is currently an Assistant Professor (Univ. Ass.) at the TU Wien’s Institute of Statistics and Mathematical Methods in Economics. His main research areas are stochastic optimization, stochastic control, optimization with PDE constraints, and bilevel optimization with applications in energy, finance and insurance. He has worked as an Assistant Professor at Vienna University and as a risk manager and consultant.
Gernot Tragleris currently an Associate Professor for Operations Research and Dean of Academic Affairs for Technical Mathematics, both at the TU Wien. His research focuses on Operations Research and mathematical methods in economics, including various methods of nonlinear and dynamic optimization, chiefly as applied to socio-economic processes and problems of energy supply and the environment. He has supervised more than fifty Master’s and Ph.D. theses and teaches several courses at the graduate level.
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