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Rectangular chance constrained geometric optimization

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Abstract

This paper discusses joint rectangular chance or probabilistic constrained geometric programs. We present a new reformulation of the joint rectangular chance constrained geometric programs where the random parameters are elliptically distributed and pairwise independent. As this reformulation is not convex, we propose new convex approximations based on the variable transformation together with piecewise linear approximation methods. For the latter, we provide a theoretical bound for the number of segments in the worst case. Our numerical results show that our approximations are asymptotically tight.

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Notes

  1. The adopted solver, SDPT3, solves efficiently the dual problems. The instance sizes are given for the dual problems.

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Acknowledgements

The authors are grateful to two anonymous reviewers for their insightful and detailed comments and suggestions, which have helped us to improve the paper significantly in both content and style. This work was supported by the Programme Cai Yuanpei under Grant No. 34593YE; National Natural Science Foundation of China under Grant No. 11571270; Fundamental Research Funds for the Central Universities under Grant No. xzy012019060.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Jia Liu, Shen Peng & Zhiping Chen

  2. Laboratoire de Recherche en Informatique (LRI), Université Paris Sud - XI, Bât. 650, 91405, Orsay Cedex, France

    Jia Liu, Shen Peng & Abdel Lisser

Authors
  1. Jia Liu
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  2. Shen Peng
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  3. Abdel Lisser
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  4. Zhiping Chen
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Correspondence to Abdel Lisser.

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Liu, J., Peng, S., Lisser, A. et al. Rectangular chance constrained geometric optimization. Optim Eng 21, 537–566 (2020). https://doi.org/10.1007/s11081-019-09460-3

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