= 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)"> = 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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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)

Suggested Citation

  • Donald J. Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Cowles Foundation Discussion Papers 1865R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2012.
    • Handle: RePEc:cwl:cwldpp:1865r
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    References listed on IDEAS

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    1. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    2. Donald J. Brown & Rosa L. Matzkin, 2008. "Testable Restrictions on the Equilibrium Manifold," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 11-25, Springer.
    3. 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.
    4. Charles Steinhorn, 2008. "Tame Topology and O-Minimal Structures," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 165-191, Springer.
    5. Donald Brown & Felix Kubler, 2008. "Computational Aspects of General Equilibrium Theory," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-76591-2, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    GE Inequalities; Polynomial solvability; Semidefinite Programming;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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