Principles of Dynamic Optimization

Piernicola Bettiol is professor of mathematics at the University of Brest, France. He received a PhD degree in mathematics from the University of Padova and was a Postdoctoral Researcher at Imperial College London. His areas of research are dynamic optimization, control theory, calculus of variations and differential games. 

Richard Vinter is Emeritus Professor of Control Theory at Imperial College, London. He obtained a PhD from Cambridge University and was a Postdoctoral Researcher (Harkness Fellowship) at M.I.T.. His research is in the areas of nonlinear analysis, dynamic optimization, systems theory, differential games, stochastic modelling and estimation.

Preface.- Overview.- Set Convergence, Measurability, and Existence of Minimizers.- Variational Principles.- Nonsmooth Analysis.- Subdifferential Calculus.- Differential Inclusions.- The Maximum Principle.- The Generalized Euler-Lagrange and Hamiltonian Inclusion Conditions.- Free End-Time Problems.- The Maximum Principle for Problems with Pathwise Constraints.- The Euler-Lagrange and Hamiltonian Inclusion Conditions in the Presence of State Constraints.- Regularity of Minimizers.- Dynamic Programming.- Bibliography.- Index.