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LEADER: 03194nam a22004575a 4500
001 013839634-5
005 20131206201129.0
008 100301s2004 xxu| s ||0| 0|eng d
020 $a9780817644130
020 $a9780817644130
020 $a9780817643362
024 7 $a10.1007/b138356$2doi
035 $a(Springer)9780817644130
040 $aSpringer
050 4 $aQA370-380
072 7 $aPBKJ$2bicssc
072 7 $aMAT007000$2bisacsh
082 04 $a515.353$223
100 1 $aCannarsa, Piermarco,$eauthor.
245 10 $aSemiconcave Functions, Hamilton—Jacobi Equations, and Optimal Control /$cby Piermarco Cannarsa, Carlo Sinestrari.
264 1 $aBoston, MA :$bBirkhäuser Boston,$c2004.
300 $aXII, 306 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aProgress in Nonlinear Differential Equations and Their Applications ;$v58
505 0 $aPreface -- A Model Problem -- Semiconcave Functions -- Generalized Gradients and Semiconcavity -- Singularities of Semiconcave Functions -- Hamilton-Jacobi Equations -- Calculus of Variations -- Optimal Control Problems -- Control Problems with Exit Time -- References -- Index.
520 $aSemiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton–Jacobi equations. The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions. A central role in the present work is reserved for the study of singularities. Singularities are first investigated for general semiconcave functions, then sharply estimated for solutions of Hamilton–Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems. Researchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions. Graduate students will profit from this text as it provides a handy—yet rigorous—introduction to modern dynamic programming for nonlinear control systems.
650 20 $aDifferential equations, Partial.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aDifferential equations, partial.
650 0 $aMathematical optimization.
650 24 $aMeasure and Integration.
650 24 $aOptimization.
700 1 $aSinestrari, Carlo,$eauthor.
776 08 $iPrinted edition:$z9780817643362
830 0 $aProgress in Nonlinear Differential Equations and Their Applications ;$v58.
988 $a20131119
906 $0VEN