03731nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001800153050001400171072001600185072002300201072001500224100008200239245010700321250001800428264006900446300004600515336002600561337002600587338003600613347002400649490005100673505054900724520138901273650003102662650002802693650002302721650001902744650002002763650004502783650002302828650002902851700008002880710003402960773002602994776003603020776003603056776003603092830005103128856004603179978-3-031-50089-3DE-He21320251030112319.0cr nn 008mamaa240619s2024    sz |    s    |||| 0|eng d  a97830315008937 a10.1007/978-3-031-50089-32doi 4aQA402.5-402.6 4aQA315-316 7aPBU2bicssc 7aMAT0420002bisacsh 7aPBU2thema1 aBettiol, Piernicola.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aPrinciples of Dynamic Optimizationh[electronic resource] /cby Piernicola Bettiol, Richard B. Vinter.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVIII, 769 p. 15 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Monographs in Mathematics,x2196-99220 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.  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. 0aMathematical optimization. 0aCalculus of variations. 0aDynamical systems. 0aSystem theory. 0aControl theory.14aCalculus of Variations and Optimization.24aDynamical Systems.24aSystems Theory, Control.1 aVinter, Richard B.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303150088608iPrinted edition:z978303150090908iPrinted edition:z9783031500916 0aSpringer Monographs in Mathematics,x2196-992240uhttps://doi.org/10.1007/978-3-031-50089-3