메뉴 건너뛰기




Volumn 37, Issue 4, 1999, Pages 1273-1290

Pontryagin maximum principle for optimal control of variational inequalities

Author keywords

[No Author keywords available]

Indexed keywords

PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

EID: 0032643046     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997328087     Document Type: Article
Times cited : (26)

References (24)
  • 2
    • 0003510879 scopus 로고
    • Analysis and control of non linear infinite dimensional systems
    • Academic Press, New York
    • V. BARBU, Analysis and Control of Non Linear Infinite Dimensional Systems, Math. Sci. Engrg. 190, Academic Press, New York, 1993.
    • (1993) Math. Sci. Engrg. , vol.190
    • Barbu, V.1
  • 3
    • 0031674233 scopus 로고    scopus 로고
    • Optimal control of problems governed by abstract elliptic variational inequalities with state constraints
    • M. BERGOUNIOUX, Optimal control of problems governed by abstract elliptic variational inequalities with state constraints, SIAM J. Control Optim., 36 (1998), pp. 273-289.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 273-289
    • Bergounioux, M.1
  • 4
    • 0001204135 scopus 로고    scopus 로고
    • Optimality conditions and generalized bang-bang principle for a state constrained semilinear parabolic problem
    • M. BERGOUNIOUX AND F. TRÖLTZSCH, Optimality conditions and generalized bang-bang principle for a state constrained semilinear parabolic problem, Numer. Funct. Anal. Optim., 15 (1996), pp. 517-537.
    • (1996) Numer. Funct. Anal. Optim. , vol.15 , pp. 517-537
    • Bergounioux, M.1    Tröltzsch, F.2
  • 5
    • 0001654425 scopus 로고
    • An extension of Pontryagin's principle for state constrained optimal control of semilinear elliptic equations and variational inequalities
    • F. BONNANS AND E. CASAS, An extension of Pontryagin's principle for state constrained optimal control of semilinear elliptic equations and variational inequalities, SIAM J. Control Optim., 33 (1995), pp. 274-298.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 274-298
    • Bonnans, F.1    Casas, E.2
  • 6
    • 0000252772 scopus 로고
    • Pontryagin's principle in the control of semilinear elliptic variational inequalities
    • J. F. BONNANS AND D. TIBA, Pontryagin's principle in the control of semilinear elliptic variational inequalities, Appl. Math. Optim., 23 (1991), pp. 299-312.
    • (1991) Appl. Math. Optim. , vol.23 , pp. 299-312
    • Bonnans, J.F.1    Tiba, D.2
  • 10
    • 0001168467 scopus 로고
    • On the local behavior of solutions of degenerate parabolic equations with measurable coefficients
    • E. DI BENEDETTO, On the local behavior of solutions of degenerate parabolic equations with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (13), (1986), pp. 487-535.
    • (1986) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (13) , pp. 487-535
    • Di Benedetto, E.1
  • 11
    • 0003823736 scopus 로고
    • Geometry of Banach spaces-selected topics
    • Springer-Verlag, Berlin, Heidelberg, New York
    • J. DIESTEL, Geometry of Banach Spaces-Selected Topics, Lecture Notes in Math. 485, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
    • (1975) Lecture Notes in Math. , vol.485
    • Diestel, J.1
  • 12
    • 0016092731 scopus 로고
    • On the variational principle
    • I. EKELAND, On the variational principle, J. Math. Anal. Appl., 47 (1974), pp. 324-353.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 324-353
    • Ekeland, I.1
  • 14
    • 84973966012 scopus 로고
    • Necessary and sufficient conditions for optimal controls in viscous flow problems
    • H. O. FATTORINI AND S. SRITHARAN, Necessary and sufficient conditions for optimal controls in viscous flow problems, Proc. Roy. Soc. Edinburgh Sect. A, 124 (1994), pp. 211-251.
    • (1994) Proc. Roy. Soc. Edinburgh Sect. A , vol.124 , pp. 211-251
    • Fattorini, H.O.1    Sritharan, S.2
  • 17
    • 0004524615 scopus 로고
    • Optimal control in some variational inequalities
    • F. MIGNOT AND J.-P. PUEL, Optimal Control in Some Variational Inequalities, Math. Cont. Theo., 14 (1985), pp. 409-422.
    • (1985) Math. Cont. Theo. , vol.14 , pp. 409-422
    • Mignot, F.1    Puel, J.-P.2
  • 18
    • 51249192154 scopus 로고
    • A variational inequality with mixed boundary conditions
    • M. K. V. MURTY AND G. STAMPACCHIA, A variational inequality with mixed boundary conditions, Israel J. Math., 13 (1972), pp. 188-224.
    • (1972) Israel J. Math. , vol.13 , pp. 188-224
    • Murty, M.K.V.1    Stampacchia, G.2
  • 19
    • 0031511775 scopus 로고    scopus 로고
    • Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints
    • J. P. RAYMOND, Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints, Discontinuous Continuous Dynam. Systems, 9 (1997), pp. 341-370.
    • (1997) Discontinuous Continuous Dynam. Systems , vol.9 , pp. 341-370
    • Raymond, J.P.1
  • 20
    • 0033102255 scopus 로고    scopus 로고
    • Hamiltonian Pontryagin's principles for control problems governed by semilinear parabolic equations
    • J. P. RAYMOND AND H. ZIDANI, Hamiltonian Pontryagin's principles for control problems governed by semilinear parabolic equations, Appl. Math. Optim., 39 (1999), pp. 143-177.
    • (1999) Appl. Math. Optim. , vol.39 , pp. 143-177
    • Raymond, J.P.1    Zidani, H.2
  • 21
    • 0032206291 scopus 로고    scopus 로고
    • Pontryagin's principles for state-constrained control problems governed by parabolic equations with unbounded controls
    • J. P. RAYMOND AND H. ZIDANI, Pontryagin's principles for state-constrained control problems governed by parabolic equations with unbounded controls, SIAM J. Control Optim., 36 (1998), pp. 1853-1871.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1853-1871
    • Raymond, J.P.1    Zidani, H.2
  • 22
    • 0003235264 scopus 로고
    • Optimal control of nonsmooth distributed parameter systems
    • Springer-Verlag, Berlin
    • D. TIBA, Optimal Control of Nonsmooth Distributed Parameter Systems, Lecture Notes in Math. 1459, Springer-Verlag, Berlin, 1990.
    • (1990) Lecture Notes in Math. , vol.1459
    • Tiba, D.1
  • 23
    • 84972537249 scopus 로고
    • Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints
    • J. YONG, Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints, Differential Integral Equations, 5 (1992), pp. 1307-1334.
    • (1992) Differential Integral Equations , vol.5 , pp. 1307-1334
    • Yong, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.