04137nam a22006015i 4500 978-3-031-50089-3 DE-He213 20251030112319.0 cr nn 008mamaa 240619s2024 sz | s |||| 0|eng d 9783031500893 978-3-031-50089-3 10.1007/978-3-031-50089-3 doi QA402.5-402.6 QA315-316 PBU bicssc MAT042000 bisacsh PBU thema Bettiol, Piernicola. author. aut http://id.loc.gov/vocabulary/relators/aut 78896 Principles of Dynamic Optimization [electronic resource] / by Piernicola Bettiol, Richard B. Vinter. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVIII, 769 p. 15 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Monographs in Mathematics, 2196-9922 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. This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle. This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics. Mathematical optimization. 65522 Calculus of variations. 67268 Dynamical systems. System theory. 66519 Control theory. 68675 Calculus of Variations and Optimization. 67270 Dynamical Systems. Systems Theory, Control. 68676 Vinter, Richard B. author. aut http://id.loc.gov/vocabulary/relators/aut 78897 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031500886 Printed edition: 9783031500909 Printed edition: 9783031500916 Springer Monographs in Mathematics, 2196-9922 73001 https://doi.org/10.1007/978-3-031-50089-3 ZDB-2-SMA ZDB-2-SXMS 60823 60823