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Blocks of coordinates, stochastic programming, and markets

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  • Sjur Didrik Flåm

    (University of Bergen)

Abstract

Considered here are extremal convolutions concerned with allocative efficiency, risk sharing, or market equilibrium. Each additive term is upper semicontinuous, proper concave, maybe non-smooth, and possibly extended-valued. In a leading interpretation, each term, alongside its block of coordinates, is controlled by an independent economic agent. Vectors are construed as contingent claims or as bundles of commodities. These are diverse, divisible, and perfectly transferable. At every stage two randomly selected agents make bilateral direct exchanges. The amounts transferred between the two parties depend on the difference between their generalized gradients. The resulting process—and the associated convergence analysis—fits the frames of stochastic programming. Motivation stems from exchange markets.

Suggested Citation

  • Sjur Didrik Flåm, 2019. "Blocks of coordinates, stochastic programming, and markets," Computational Management Science, Springer, vol. 16(1), pages 3-16, February.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0303-3
    DOI: 10.1007/s10287-018-0303-3
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    References listed on IDEAS

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    1. Sjur Didrik Flåm & Kjetil Gramstad, 2012. "Direct Exchange In Linear Economies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 1-18.
    2. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Ion Necoara & Yurii Nesterov & François Glineur, 2017. "Random Block Coordinate Descent Methods for Linearly Constrained Optimization over Networks," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 227-254, April.
    4. Yurii Nesterov & Vladimir Shikhman, 2017. "Distributed Price Adjustment Based on Convex Analysis," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 594-622, February.
    5. Flåm, Sjur Didrik & Gramstad, Kjetil, 2012. "Direct Exchange in Linear Economies," Working Papers in Economics 05/12, University of Bergen, Department of Economics.
    6. Alois Pichler, 2017. "A quantitative comparison of risk measures," Annals of Operations Research, Springer, vol. 254(1), pages 251-275, July.
    7. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    8. Yurii NESTEROV & Vladimir SHIKHMAN, 2017. "Distributed price adjustment based on convex analysis," LIDAM Reprints CORE 2832, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. L. Xiao & S. Boyd, 2006. "Optimal Scaling of a Gradient Method for Distributed Resource Allocation," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 469-488, June.
    10. Ion Necoara & Andrei Patrascu, 2014. "A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 307-337, March.
    11. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
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