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Cascading: an adjusted exchange method for robust conic programming

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  • Ralf Werner

Abstract

It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769–805, 1998) increases the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced in Kočvara et al. (Comput Struct 76:431–442, 2000) an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust conic problem. Copyright Springer-Verlag 2008

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  • Ralf Werner, 2008. "Cascading: an adjusted exchange method for robust conic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 179-189, June.
    • Handle: RePEc:spr:cejnor:v:16:y:2008:i:2:p:179-189
    DOI: 10.1007/s10100-007-0047-6
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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    4. S. Y. Wu & S. C. Fang & C. J. Lin, 1998. "Relaxed Cutting Plane Method for Solving Linear Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 759-779, December.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    8. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    Cited by:

    1. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    2. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    3. Ayşe Özmen & Yuriy Zinchenko & Gerhard-Wilhelm Weber, 2023. "Robust multivariate adaptive regression splines under cross-polytope uncertainty: an application in a natural gas market," Annals of Operations Research, Springer, vol. 324(1), pages 1337-1367, May.
    4. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.

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