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Volumn 243, Issue 2, 2007, Pages 256-269

Normality of the maximum principle for nonconvex constrained Bolza problems

Author keywords

Bolza problem; Constrained maximum principle; Normal necessary conditions; Optimal control

Indexed keywords


EID: 36048968848     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.05.005     Document Type: Article
Times cited : (28)

References (24)
  • 1
    • 0000467856 scopus 로고
    • Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
    • Ambrosio L., Ascenzi O., and Buttazzo G. Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. J. Math. Anal. Appl. 143 (1989) 301-316
    • (1989) J. Math. Anal. Appl. , vol.143 , pp. 301-316
    • Ambrosio, L.1    Ascenzi, O.2    Buttazzo, G.3
  • 2
    • 0031140636 scopus 로고    scopus 로고
    • Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints
    • Arutyanov A.V., and Aseev S.M. Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints. SIAM J. Control Optim. 35 (1997) 930-952
    • (1997) SIAM J. Control Optim. , vol.35 , pp. 930-952
    • Arutyanov, A.V.1    Aseev, S.M.2
  • 5
    • 36049012836 scopus 로고    scopus 로고
    • P. Bettiol, H. Frankowska, Hölder continuity of adjoint states and optimal controls for state constrained problems, Appl. Math. Optim., in press
  • 6
    • 77950682766 scopus 로고    scopus 로고
    • P. Cannarsa, H. Frankowska, E. Marchini, Existence and Lipschitz regularity of solutions to Bolza problems in optimal control, submitted for publication
  • 7
    • 0742288932 scopus 로고    scopus 로고
    • The classical problem of the calculus of variations in the autonomous case: Relaxation and lipschitzianity of solutions
    • Cellina A. The classical problem of the calculus of variations in the autonomous case: Relaxation and lipschitzianity of solutions. Trans. Amer. Math. Soc. 356 1 (2004) 415-426
    • (2004) Trans. Amer. Math. Soc. , vol.356 , Issue.1 , pp. 415-426
    • Cellina, A.1
  • 8
    • 0347354935 scopus 로고    scopus 로고
    • Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case
    • Cellina A., and Ferriero A. Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case. Ann. Inst. H. Poincaré Anal. Non Linéaire 20 6 (2003) 911-919
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.6 , pp. 911-919
    • Cellina, A.1    Ferriero, A.2
  • 9
    • 33644945659 scopus 로고    scopus 로고
    • A connection between the maximum principle and dynamic programming for constrained control problems
    • Cernea A., and Frankowska H. A connection between the maximum principle and dynamic programming for constrained control problems. SIAM J. Control Optim. 44 (2005) 673-703
    • (2005) SIAM J. Control Optim. , vol.44 , pp. 673-703
    • Cernea, A.1    Frankowska, H.2
  • 11
    • 0025460640 scopus 로고
    • Regularity properties of optimal controls
    • Clarke F., and Vinter R. Regularity properties of optimal controls. SIAM J. Control Optim. 28 4 (1990) 980-997
    • (1990) SIAM J. Control Optim. , vol.28 , Issue.4 , pp. 980-997
    • Clarke, F.1    Vinter, R.2
  • 12
    • 11944253919 scopus 로고    scopus 로고
    • Autonomous integral functionals with discontinuous nonconvex integrands: Lipschitz regularity of minimizers, DuBois-Reymond necessary conditions, and Hamilton-Jacobi equations
    • Dal Maso G., and Frankowska H. Autonomous integral functionals with discontinuous nonconvex integrands: Lipschitz regularity of minimizers, DuBois-Reymond necessary conditions, and Hamilton-Jacobi equations. Appl. Math. Optim. 48 1 (2003) 39-66
    • (2003) Appl. Math. Optim. , vol.48 , Issue.1 , pp. 39-66
    • Dal Maso, G.1    Frankowska, H.2
  • 13
    • 0004152311 scopus 로고    scopus 로고
    • Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints
    • Ferreira M.M.A., Fontes F.A.C.C., and Vinter R.B. Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints. J. Math. Anal. Appl. 233 (1999) 116-129
    • (1999) J. Math. Anal. Appl. , vol.233 , pp. 116-129
    • Ferreira, M.M.A.1    Fontes, F.A.C.C.2    Vinter, R.B.3
  • 14
    • 33747704221 scopus 로고    scopus 로고
    • Regularity of minimizers and of adjoint states in optimal control under state constraints
    • Frankowska H. Regularity of minimizers and of adjoint states in optimal control under state constraints. J. Convex Anal. 13 2 (2006) 299-328
    • (2006) J. Convex Anal. , vol.13 , Issue.2 , pp. 299-328
    • Frankowska, H.1
  • 15
    • 33749241493 scopus 로고    scopus 로고
    • Lipschitzianity of optimal trajectories for the Bolza optimal control problem
    • Frankowska H., and Marchini E. Lipschitzianity of optimal trajectories for the Bolza optimal control problem. Calc. Var. Partial Differential Equations 27 (2006) 467-492. http://www.springerlink.com/content/e5n3863602425595/
    • (2006) Calc. Var. Partial Differential Equations , vol.27 , pp. 467-492
    • Frankowska, H.1    Marchini, E.2
  • 16
    • 4944235424 scopus 로고    scopus 로고
    • Lipschitz continuity of optimal controls for state constrained problems
    • Galbraith G.N., and Vinter R.B. Lipschitz continuity of optimal controls for state constrained problems. SIAM J. Control Optim. 42 5 (2003) 1727-1744
    • (2003) SIAM J. Control Optim. , vol.42 , Issue.5 , pp. 1727-1744
    • Galbraith, G.N.1    Vinter, R.B.2
  • 19
    • 0033284727 scopus 로고    scopus 로고
    • A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control
    • Rampazzo F., and Vinter R.B. A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control. IMA 16 4 (1999) 335-351
    • (1999) IMA , vol.16 , Issue.4 , pp. 335-351
    • Rampazzo, F.1    Vinter, R.B.2
  • 20
    • 0034433933 scopus 로고    scopus 로고
    • Degenerate optimal control problems with state constraints
    • Rampazzo F., and Vinter R.B. Degenerate optimal control problems with state constraints. SIAM J. Control Optim. 39 4 (2000) 989-1007
    • (2000) SIAM J. Control Optim. , vol.39 , Issue.4 , pp. 989-1007
    • Rampazzo, F.1    Vinter, R.B.2
  • 21
    • 0034149003 scopus 로고    scopus 로고
    • Lipschitzian regularity of the minimizers for optimal control problems with control-affine dynamics
    • Sarychev A., and Torres D.F.M. Lipschitzian regularity of the minimizers for optimal control problems with control-affine dynamics. Appl. Math. Optim. 41 2 (2000) 237-254
    • (2000) Appl. Math. Optim. , vol.41 , Issue.2 , pp. 237-254
    • Sarychev, A.1    Torres, D.F.M.2
  • 22
    • 0142216445 scopus 로고    scopus 로고
    • Lipschitzian regularity of the minimizing trajectories for nonlinear optimal control problems
    • Torres D.F.M. Lipschitzian regularity of the minimizing trajectories for nonlinear optimal control problems. Math. Control Signals Systems 162 3 (2003) 158-174
    • (2003) Math. Control Signals Systems , vol.162 , Issue.3 , pp. 158-174
    • Torres, D.F.M.1
  • 24
    • 0348001128 scopus 로고
    • The maximum principle and controllability of nonlinear equations
    • Yorke J.A. The maximum principle and controllability of nonlinear equations. SIAM J. Control 10 (1972) 334-338
    • (1972) SIAM J. Control , vol.10 , pp. 334-338
    • Yorke, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.