LEADER 03975nam 22006615 450 001 9910988387603321 005 20251217112812.0 010 $a9783031500893 024 7 $a10.1007/978-3-031-50089-3 035 $a(CKB)32317310200041 035 $a(MiAaPQ)EBC31496595 035 $a(Au-PeEL)EBL31496595 035 $a(DE-He213)978-3-031-50089-3 035 $a(OCoLC)1441720212 035 $a(EXLCZ)9932317310200041 100 $a20240619d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPrinciples of Dynamic Optimization /$fby Piernicola Bettiol, Richard B. Vinter 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (789 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a9783031500886 327 $aPreface -- 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. 330 $aThis monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle. This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aMathematical optimization 606 $aCalculus of variations 606 $aDynamics 606 $aSystem theory 606 $aControl theory 606 $aCalculus of Variations and Optimization 606 $aDynamical Systems 606 $aSystems Theory, Control 606 $aProgramaciķ dināmica$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aDynamics. 615 0$aSystem theory. 615 0$aControl theory. 615 14$aCalculus of Variations and Optimization. 615 24$aDynamical Systems. 615 24$aSystems Theory, Control. 615 7$aProgramaciķ dināmica 676 $a519.6 700 $aBettiol$b Piernicola$01802448 701 $aVinter$b R. B$g(Richard B.)$056541 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910988387603321 996 $aPrinciples of Dynamic Optimization$94348116 997 $aUNINA