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Simplicial Decomposition

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References

  1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: Theory, algorithms, and applications. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  2. Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming: Theory and algorithms. Wiley, New York

    MATH  Google Scholar 

  3. Bertsekas DP (1982) Projected Newton methods for optimization problems with simple constraints. SIAM J Control Optim 20:221–246

    Article  MathSciNet  MATH  Google Scholar 

  4. Cantor DG, Gerla M (1974) Optimal routing in a packet switched network. IEEE Trans Computers c-23:1062–1069

    Article  MathSciNet  Google Scholar 

  5. Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8:101–111

    Article  MATH  Google Scholar 

  6. Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res Logist Quart 3:95–110

    Article  MathSciNet  Google Scholar 

  7. Geoffrion AM (1970) Elements of large-scale mathematical programming. Managem Sci 16:652–691

    MathSciNet  Google Scholar 

  8. Gerla M (1973) The design of store-and-forward (S/F) networks for computer communications. PhD Thesis Dept Computer Sci Univ Calif, Los Angeles

    Google Scholar 

  9. Hearn DW, Lawphongpanich S, Ventura JA (1985) Finiteness in restricted simplicial decomposition. Oper Res Lett 4:125–130

    Article  MathSciNet  MATH  Google Scholar 

  10. Hearn DW, Lawphongpanich S, Ventura JA (1987) Restricted simplicial decompsition: Computation and extension. Math Program 31:99–118

    MathSciNet  MATH  Google Scholar 

  11. Holloway C (1974) An extension of the Frank–Wolfe method of feasible directions. Math Program 6:14–27

    Article  MathSciNet  MATH  Google Scholar 

  12. Larsson T, Patriksson M (1992) Simplicial decomposition with disaggregate representation for the traffic assignment problem. Transport Sci 26:4–17

    Article  MATH  Google Scholar 

  13. Larsson T, Patriksson M, Rydergren C (1997) Applications of simplicial decomposition with nonlinear column generations to nonlinear network flows. In: Pardalos PM, Hearn DW, Hager WH (eds) Network Optimization. Lecture Notes Economics & Math Systems. Springer, Berlin, pp 346–373

    Google Scholar 

  14. Lawphongpanich S (2000) Simplicial with truncated Dantzig–Wolfe decomposition for nonlinear multicommodity network flow problems with side constraints. Oper Res Lett 26:33–41

    Article  MathSciNet  MATH  Google Scholar 

  15. Lawphongpanich S, Hearn DW (1986) Restricted simplicial decomposition with applications to the traffic assignment problem. Ricerca Oper 38:97–120

    Google Scholar 

  16. Migdalas A (1994) A regularization of the Frank–Wolfe method and unification of certain nonlinear programming method. Math Program 65:331–346

    Article  MathSciNet  Google Scholar 

  17. Mulvey J, Zenios SA, Ahlfeld DP (1990) Simplicial decomposition for convex generalized networks. J Inform Optim Sci 11:359–387

    MathSciNet  MATH  Google Scholar 

  18. Murchland JD (1970) Road network traffic distribution in equilibrium. In: Henn R, Künzi HP, Schubert H (eds) Proc. Math. Models in the Social Sci. Anton Hain Verlag, Meisenheim, pp 145–183

    Google Scholar 

  19. Powell WB (1993) On algorithms for nonlinear dynamic networks. In: Du D-Z, Pardalos PM (eds) Network Optimization Problems. World Sci., Singapore, pp 203–231

    Google Scholar 

  20. Rockafellar RT (1970) Convex analysis. Princeton Univ. Press, Princeton

    MATH  Google Scholar 

  21. Ventura JA, Hearn DW (1993) Restricted simplicial decomposition for convex constrained problems. Math Program 59:71–85

    Article  MathSciNet  Google Scholar 

  22. Von Hohenbalken B (1975) A finite algorithm to maximize certain pseudo-concave function on polytopes. Math Program 8:189–206

    Article  MathSciNet  Google Scholar 

  23. Von Hohenbalken B (1977) Simplicial decomposition in nonlinear programming algorithms. Math Program 13:49–68

    Article  MathSciNet  MATH  Google Scholar 

  24. Wu C-H, Ventura JA (1994) Restricted simplicial decomposition with side constraints and its application to capacitated multicommodity networks. In: IME Working Paper Dept. Industr. and Management Systems Engin., Penn. State Univ., vol 94-128

    Google Scholar 

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© 2008 Springer-Verlag

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Lawphongpanich, S. (2008). Simplicial Decomposition . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_614

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