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Linear Stationary Point Problems On Unbounded Polyhedra

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  • DAI, Y.
  • TALMAN, D.

Abstract

In this paper we propose a complementary pivoting algorithm for finding a stationary point of an affine function on an unbounded polyhedron. Under some mild conditions there is a piecewise linear path from an arbitrarily chosen point in the polyhedron leading to a solution of the problem. By exploiting fully the linearity of the problem, each linear piece of the path is followed in principle by making just one linear programming pivoting step.
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Suggested Citation

  • Dai, Y. & Talman, D., 1990. "Linear Stationary Point Problems On Unbounded Polyhedra," Papers 9067, Tilburg - Center for Economic Research.
    • Handle: RePEc:fth:tilbur:9067
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    References listed on IDEAS

    as
    1. Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for stationary point problems on polytopes," Other publications TiSEM 0d6b2de0-17c0-4d5e-963f-5, Tilburg University, School of Economics and Management.
    2. Dai, Y. & van der Laan, G. & Talman, A.J.J. & Yamamoto, Y., 1989. "A simplicial algorithm for the nonlinear stationary point problem on an unbounded polyhedron," Other publications TiSEM 82992276-1868-4b56-a937-0, Tilburg University, School of Economics and Management.
    3. Dai, Y., 1989. "A simplicial algorithm for the nonlinear stationary point problem of an unbounded polyhedron," Serie Research Memoranda 0068, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
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    Cited by:

    1. Talman, A.J.J. & Thijssen, J.J.J., 2006. "Existence of equilibrium and price adjustments in a finance economy with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 255-268, June.
    2. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    3. Kremers, H. & Laan, G. van der & Talman, A.J.J., 1991. "On the existence and computation of an equilibrium in an economy with constant returns to scale production," Serie Research Memoranda 0082, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.

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    Keywords

    linear models ; linear programming;

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