IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v16y2019i1d10.1007_s10287-018-0303-3.html
   My bibliography  Save this article

Blocks of coordinates, stochastic programming, and markets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-018-0303-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-018-0303-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Sjur Didrik Flåm, 2016. "Noncooperative games, coupling constraints, and partial efficiency," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 213-229, October.
    3. Andrea Cristofari, 2019. "An almost cyclic 2-coordinate descent method for singly linearly constrained problems," Computational Optimization and Applications, Springer, vol. 73(2), pages 411-452, June.
    4. Jin Zhang & Xide Zhu, 2022. "Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 564-597, February.
    5. Flåm, Sjur Didrik, 2015. "Bilateral exchange and competitive equilibrium," Working Papers in Economics 05/15, University of Bergen, Department of Economics.
    6. Rachael Tappenden & Peter Richtárik & Jacek Gondzio, 2016. "Inexact Coordinate Descent: Complexity and Preconditioning," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 144-176, July.
    7. 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.
    8. Kimon Fountoulakis & Rachael Tappenden, 2018. "A flexible coordinate descent method," Computational Optimization and Applications, Springer, vol. 70(2), pages 351-394, June.
    9. Mingyi Hong & Tsung-Hui Chang & Xiangfeng Wang & Meisam Razaviyayn & Shiqian Ma & Zhi-Quan Luo, 2020. "A Block Successive Upper-Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 833-861, August.
    10. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
    11. Sjur Didrik Flåm, 2020. "Emergence of price-taking Behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 847-870, October.
    12. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization," Computational Optimization and Applications, Springer, vol. 79(3), pages 681-715, July.
    13. Tao Sun & Yuejiao Sun & Yangyang Xu & Wotao Yin, 2020. "Markov chain block coordinate descent," Computational Optimization and Applications, Springer, vol. 75(1), pages 35-61, January.
    14. Yangyang Xu, 2019. "Asynchronous parallel primal–dual block coordinate update methods for affinely constrained convex programs," Computational Optimization and Applications, Springer, vol. 72(1), pages 87-113, January.
    15. Cassioli, A. & Di Lorenzo, D. & Sciandrone, M., 2013. "On the convergence of inexact block coordinate descent methods for constrained optimization," European Journal of Operational Research, Elsevier, vol. 231(2), pages 274-281.
    16. Sjur Didrik Flåm, 2024. "Via Order Markets Towards Price-Taking Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 977-994, June.
    17. David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.
    18. Flåm, Sjur Didrik, 2016. "Borch’s theorem, equal margins, and efficient allocation," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 162-168.
    19. Andrei Patrascu & Ion Necoara, 2015. "Efficient random coordinate descent algorithms for large-scale structured nonconvex optimization," Journal of Global Optimization, Springer, vol. 61(1), pages 19-46, January.
    20. Qin Wang & Weiguo Li & Wendi Bao & Feiyu Zhang, 2022. "Accelerated Randomized Coordinate Descent for Solving Linear Systems," Mathematics, MDPI, vol. 10(22), pages 1-20, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:16:y:2019:i:1:d:10.1007_s10287-018-0303-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.