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Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks

Author

Listed:
  • F. Maggioni

    (University of Bergamo)

  • F. A. Potra

    (University of Maryland)

  • M. I. Bertocchi

    (University of Bergamo)

  • E. Allevi

    (University of Brescia)

Abstract

We propose a two-stage stochastic second-order cone programming formulation of the semidefinite stochastic location-aided routing (SLAR) model, described in Ariyawansa and Zhu (Q. J. Oper. Res. 4(3), 239–253, 2006). The aim is to provide a sender node S with an algorithm for optimally determining a region that is expected to contain a destination node D (the expected zone). The movements of the destination node are represented by ellipsoid scenarios, randomly generated by uniform and normal distributions in a neighborhood of the starting position of the destination node. By using a second-order cone model, we are able to solve problems with a much larger number of scenarios (20250) than it is possible with the semidefinite model (500). The use of a larger number of scenarios allows for the computation of a new expected zone, that may be very effective in practical applications, and for obtaining stability results for the optimal first-stage solutions and the optimal cost function values.

Suggested Citation

  • F. Maggioni & F. A. Potra & M. I. Bertocchi & E. Allevi, 2009. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 309-328, November.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:2:d:10.1007_s10957-009-9561-0
    DOI: 10.1007/s10957-009-9561-0
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    Citations

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    Cited by:

    1. Luca Bertazzi & Francesca Maggioni, 2015. "Solution Approaches for the Stochastic Capacitated Traveling Salesmen Location Problem with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 321-342, July.
    2. Qingsong Duan & Mengwei Xu & Shaoyan Guo & Liwei Zhang, 2018. "Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    3. Francesca Maggioni & Stein Wallace, 2012. "Analyzing the quality of the expected value solution in stochastic programming," Annals of Operations Research, Springer, vol. 200(1), pages 37-54, November.
    4. Baha Alzalg, 2016. "The Algebraic Structure of the Arbitrary-Order Cone," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 32-49, April.
    5. Baha Alzalg, 2014. "Homogeneous Self-dual Algorithms for Stochastic Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 148-164, October.
    6. Shuang Chen & Li-Ping Pang & Xue-Fei Ma & Dan Li, 2016. "SAA method based on modified Newton method for stochastic variational inequality with second-order cone constraints and application in portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 129-154, August.
    7. Alzalg, Baha, 2015. "Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 494-508.
    8. Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    9. Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.

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