000 04137nam a22006015i 4500
001 978-3-031-50089-3
003 DE-He213
005 20251030112319.0
007 cr nn 008mamaa
008 240619s2024 sz | s |||| 0|eng d
020 _a9783031500893
_9978-3-031-50089-3
024 7 _a10.1007/978-3-031-50089-3
_2doi
050 4 _aQA402.5-402.6
050 4 _aQA315-316
072 7 _aPBU
_2bicssc
072 7 _aMAT042000
_2bisacsh
072 7 _aPBU
_2thema
100 1 _aBettiol, Piernicola.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978896
245 1 0 _aPrinciples of Dynamic Optimization
_h[electronic resource] /
_cby Piernicola Bettiol, Richard B. Vinter.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVIII, 769 p. 15 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x2196-9922
505 0 _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.
520 _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.
650 0 _aMathematical optimization.
_965522
650 0 _aCalculus of variations.
_967268
650 0 _aDynamical systems.
650 0 _aSystem theory.
_966519
650 0 _aControl theory.
_968675
650 1 4 _aCalculus of Variations and Optimization.
_967270
650 2 4 _aDynamical Systems.
650 2 4 _aSystems Theory, Control.
_968676
700 1 _aVinter, Richard B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978897
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031500886
776 0 8 _iPrinted edition:
_z9783031500909
776 0 8 _iPrinted edition:
_z9783031500916
830 0 _aSpringer Monographs in Mathematics,
_x2196-9922
_973001
856 4 0 _uhttps://doi.org/10.1007/978-3-031-50089-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60823
_d60823