메뉴 건너뛰기




Volumn 33, Issue 4, 2008, Pages 821-838

Label-setting methods for multimode stochastic shortest path problems on graphs

Author keywords

Dial's method; Dijkstra's method; Dynamic programming; Fast marching method; Hamilton Jacobi PDEs; Label setting; Optimal control; Stochastic shortest path

Indexed keywords

DIAL'S METHOD; DIJKSTRA'S METHOD; FAST MARCHING METHOD; HAMILTON-JACOBI PDES; OPTIMAL CONTROL; STOCHASTIC SHORTEST PATH;

EID: 61449153735     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1080.0321     Document Type: Article
Times cited : (18)

References (35)
  • 2
    • 61449185827 scopus 로고    scopus 로고
    • Fast marching methods for a class of anisotropic stationary Hamilton-Jacobi equations
    • Technical Report TR-2006-27, Department of Computer Science, University of British Columbia
    • Alton, K., I. M. Mitchell. 2007. Fast marching methods for a class of anisotropic stationary Hamilton-Jacobi equations. Technical Report TR-2006-27, Department of Computer Science, University of British Columbia.
    • (2007)
    • Alton, K.1    Mitchell, I.M.2
  • 5
    • 0003161907 scopus 로고
    • An analysis of stochastic shortest path problems
    • Bertsekas, D. P., J. N. Tsitsiklis. 1991. An analysis of stochastic shortest path problems. Math. Oper: Res. 16(3) 580-595.
    • (1991) Math. Oper: Res , vol.16 , Issue.3 , pp. 580-595
    • Bertsekas, D.P.1    Tsitsiklis, J.N.2
  • 7
    • 38549129333 scopus 로고    scopus 로고
    • On the speed of convergence of value iteration on stochastic shortest-path problems
    • Bonet, B. 2007. On the speed of convergence of value iteration on stochastic shortest-path problems. Math. Oper. Res. 32(2) 365-373.
    • (2007) Math. Oper. Res , vol.32 , Issue.2 , pp. 365-373
    • Bonet, B.1
  • 8
    • 33746085983 scopus 로고    scopus 로고
    • Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle
    • Bornemann, F., C. Rasch. 2006. Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle. Comput. visualization Sci. 9(2) 57-69.
    • (2006) Comput. visualization Sci , vol.9 , Issue.2 , pp. 57-69
    • Bornemann, F.1    Rasch, C.2
  • 10
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • Crandall, M. G., P.-L. Lions. 1983. Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer: Math. Soc. 277(1) 1-42.
    • (1983) Trans. Amer: Math. Soc , vol.277 , Issue.1 , pp. 1-42
    • Crandall, M.G.1    Lions, P.-L.2
  • 11
    • 84945708671 scopus 로고
    • Algorithm 360: Shortest path, forest with topological ordering
    • Dial, R. 1969. Algorithm 360: Shortest path, forest with topological ordering. Comm. ACM 12(11) 632-633.
    • (1969) Comm. ACM , vol.12 , Issue.11 , pp. 632-633
    • Dial, R.1
  • 12
    • 34147120474 scopus 로고
    • A note on two problems in connection with, graphs
    • Dijkstra, E. W. 1959. A note on two problems in connection with, graphs. Numerische Mathematik 1 269-271.
    • (1959) Numerische Mathematik , vol.1 , pp. 269-271
    • Dijkstra, E.W.1
  • 13
    • 0023123237 scopus 로고
    • A numerical approach to the infinite horizon problem of deterministic control theory
    • 1-13; corrigenda 23 () 213-214
    • Falcone, M. 1987. A numerical approach to the infinite horizon problem of deterministic control theory. Appl. Math. Optim. 15(1) 1-13; corrigenda 23 (1991) 213-214.
    • (1987) Appl. Math. Optim , vol.15 , Issue.1
    • Falcone, M.1
  • 14
    • 0022027092 scopus 로고
    • On deterministic control problems: An approximate procedure for the optimal cost, part I: The stationary problem
    • Gonzales, R., E. Rofman. 1985. On deterministic control problems: An approximate procedure for the optimal cost, part I: The stationary problem. SIAM J. Control Optim. 23(2) 242-266.
    • (1985) SIAM J. Control Optim , vol.23 , Issue.2 , pp. 242-266
    • Gonzales, R.1    Rofman, E.2
  • 15
    • 0035679975 scopus 로고    scopus 로고
    • An O(N) level set method for Eikonal equations
    • Kim, S. 2001. An O(N) level set method for Eikonal equations. SIAM J. Sci. Comput. 22(6) 2178-2193.
    • (2001) SIAM J. Sci. Comput , vol.22 , Issue.6 , pp. 2178-2193
    • Kim, S.1
  • 16
    • 0001140342 scopus 로고    scopus 로고
    • Fast marching methods on triangulated domains
    • Kimmel, R., J. A. Sethian. 1998. Fast marching methods on triangulated domains. Proc. Nat. Acad. Sci. 95(15) 8341-8435.
    • (1998) Proc. Nat. Acad. Sci , vol.95 , Issue.15 , pp. 8341-8435
    • Kimmel, R.1    Sethian, J.A.2
  • 17
    • 0037249094 scopus 로고    scopus 로고
    • Numerical approximations for stochastic differential games
    • Kushner, H. J. 2002. Numerical approximations for stochastic differential games. SIAM J. Control Optim. 41(2) 457-486.
    • (2002) SIAM J. Control Optim , vol.41 , Issue.2 , pp. 457-486
    • Kushner, H.J.1
  • 19
    • 0000653947 scopus 로고    scopus 로고
    • Level Set Methods: An Over-view and Some Recent Results
    • Osher, S., R. P. Fedkiw. 2001. Level Set Methods: An Over-view and Some Recent Results. J. Comput. Phys. 169 463-502.
    • (2001) J. Comput. Phys , vol.169 , pp. 463-502
    • Osher, S.1    Fedkiw, R.P.2
  • 20
  • 23
    • 0029966538 scopus 로고    scopus 로고
    • A fast marching level set method for monotonically advancing fronts
    • Sethian, J. A. 1996a. A fast marching level set method for monotonically advancing fronts. Proc. National Acad. Sci. 93(4) 1591-1595.
    • (1996) Proc. National Acad. Sci , vol.93 , Issue.4 , pp. 1591-1595
    • Sethian, J.A.1
  • 25
    • 0032631799 scopus 로고    scopus 로고
    • Fast marching methods
    • Sethian, J. A. 1999. Fast marching methods. SIAM Rev. 41(2) 199-235.
    • (1999) SIAM Rev , vol.41 , Issue.2 , pp. 199-235
    • Sethian, J.A.1
  • 26
    • 0034705102 scopus 로고    scopus 로고
    • Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes
    • Sethian, J. A., A. Vladimirsky. 2000. Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes. Proc. National Acad. Sci. 97(11) 5699-5703.
    • (2000) Proc. National Acad. Sci , vol.97 , Issue.11 , pp. 5699-5703
    • Sethian, J.A.1    Vladimirsky, A.2
  • 27
    • 0035949589 scopus 로고    scopus 로고
    • Ordered upwind methods for static Hamilton-Jacobi equations
    • Sethian, J. A., A. Vladimirsky. 2001. Ordered upwind methods for static Hamilton-Jacobi equations. Proc. National Acad. Sci. 98(20) 11069-11074.
    • (2001) Proc. National Acad. Sci , vol.98 , Issue.20 , pp. 11069-11074
    • Sethian, J.A.1    Vladimirsky, A.2
  • 29
    • 1842511489 scopus 로고    scopus 로고
    • Ordered upwind methods for static Hamilton-Jacobi equations: Theory and Algorithms
    • Sethian, J. A., A. Vladimirsky. 2003. Ordered upwind methods for static Hamilton-Jacobi equations: Theory and Algorithms. SIAM J. Numer. Anal. 41(1) 325-363.
    • (2003) SIAM J. Numer. Anal , vol.41 , Issue.1 , pp. 325-363
    • Sethian, J.A.1    Vladimirsky, A.2
  • 31
    • 0038380608 scopus 로고    scopus 로고
    • Second-order numerical methods for first-order Hamilton-Jacobi equations
    • Szpiro, A., P. Dupuis. 2002. Second-order numerical methods for first-order Hamilton-Jacobi equations. SIAM J. Numer. Anal. 40(3) 1136-1183.
    • (2002) SIAM J. Numer. Anal , vol.40 , Issue.3 , pp. 1136-1183
    • Szpiro, A.1    Dupuis, P.2
  • 32
    • 0028738762 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • Lake Buena Vista, FL
    • Tsitsiklis, J. N. 1994. Efficient algorithms for globally optimal trajectories. Proc. IEEE 33rd Conf. Decision and Control, Lake Buena Vista, FL, 1368-1373.
    • (1994) Proc. IEEE 33rd Conf. Decision and Control , pp. 1368-1373
    • Tsitsiklis, J.N.1
  • 33
    • 0029373106 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • Tsitsiklis, J. N. 1995. Efficient algorithms for globally optimal trajectories. IEEE Trans. Automatic Control 40(9) 1528-1538.
    • (1995) IEEE Trans. Automatic Control , vol.40 , Issue.9 , pp. 1528-1538
    • Tsitsiklis, J.N.1
  • 35
    • 29144489240 scopus 로고    scopus 로고
    • O(N) implementation of the fast marching algorithm
    • Yatziv, L., A. Bartesaghi, G. Sapiro. 2006. O(N) implementation of the fast marching algorithm. J. Comput. Phys. 212(2) 393-399.
    • (2006) J. Comput. Phys , vol.212 , Issue.2 , pp. 393-399
    • Yatziv, L.1    Bartesaghi, A.2    Sapiro, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.