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Notes on Computational Complexity of GE Inequalities

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    Abstract

    This paper is a revision of my paper, CFDP 1865. The principal innovation is an equivalent reformulation of the decision problem for weak feasibility of the GE inequalities, using polynomial time ellipsoid methods, as a semidefinite optimization problem, using polynomial time interior point methods. We minimize the maximum of the Euclidean distances between the aggregate endowment and the Minkowski sum of the sets of consumer's Marshallian demands in each observation. We show that this is an instance of the generic semidefinite optimization problem: inf_{x in K}f(x) equivalent to Opt(K,f), the optimal value of the program, where the convex feasible set K and the convex objective function f(x) have semidefinite representations. This problem can be approximately solved in polynomial time. That is, if p(K,x) is a convex measure of infeasibilty, where for all x, p(K,x) >= 0 and p(K,z) = 0 iff z in K, then for every epsilon > 0 there exists an epsilon-optimal y such that p(K,y)

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    File URL: http://cowles.econ.yale.edu/P/cd/d18b/d1865-r.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1865R.

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    Length: 19 pages
    Date of creation: Jul 2012
    Date of revision: Aug 2012
    Handle: RePEc:cwl:cwldpp:1865r

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    Related research

    Keywords: GE Inequalities; Polynomial solvability; Semidefinite Programming;

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    1. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers 1109, Cowles Foundation for Research in Economics, Yale University.
    2. Donald J. Brown & Chris Shannon, 2000. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," Econometrica, Econometric Society, vol. 68(6), pages 1529-1540, November.
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