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Distributionally robust chance constrained problem under interval distribution information

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Abstract

This paper is concerned with distributionally robust chance constrained problem under interval distribution information. Using worst-case CVaR approximation, we present a tractable convex programming approximation for distributionally robust individual chance constrained problem under interval sets of mean and covariance information. We prove the worst-case CVaR approximation problem is an exact form of the distributionally robust individual chance constrained problem. Then, our result is applied to worst-case Value-at-Risk optimization problem. Moreover, we discuss the problem under several ambiguous distribution information and investigate tractable approximations for distributionally robust joint chance constrained problem. Finally, we provide an illustrative example to show our results.

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References

  1. Ahmed, S.: Convex relaxations of chance constrained optimization problems. Optim. Lett. 8(1), 1–12 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bertsimas, D., Brown, D.B., Caramanis, C.: Theory and application of robust optimization. SIAM Rev. 53(3), 464–501 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Calafiore, G., EI Ghaoui, L.: Distributionally robust chance-constrained linear programms with applications. J. Optim. Theory Appl. 130(1), 1–22 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, W., Sim, M., Sun, J., Teo, C.P.: From CVaR to uncertainy set: implicaions in joint chance constrained optimization. Oper. Res. 55(6), 470–485 (2010)

    Article  MATH  Google Scholar 

  5. Delage, E., Ye, Y.: Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3), 595–612 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. El Ghaoui, L., Oks, M., Oustry, F.: Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper. Res. 51(4), 543–556 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Math. Prog. 39, 117–129 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Natarajan, K., Sim, M., Uichanco, J.: Tractable robust expected utility and risk models for portofolio optimization. Math. Finance 20(4), 695–731 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nemirovski, A., Shapiro, A.: Convex approximation of chance constrained programms. SIAM J. Optim. 17(4), 969–996 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shapiro, A., Dentcheva, D., Ruszczyński, A.: Lecture on Stochastic Programming: Modeling and Theory. MOS-SIAM Series on Optimization. SIAM, Philadelphia (2009)

    Book  MATH  Google Scholar 

  11. Xu, H., Caramanis, C., Mannor, S.: Optimization under probabilistic envelope constraints. Oper. Res. 60(3), 682–699 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yang, W., Xu, H.: Distributionally robust chance constraints for non-linear uncertainties. Math. Prog. Ser. A 155(1), 231–265 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zymler, S., Kuhn, D., Rustem, B.: Distributionally robust joint chance constraints with second-order moment information. Math. Prog. Ser. A 137(1), 167–198 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Ke-wei Ding, Ming-hui Wang & Nan-jing Huang

  2. Department of Foundation Education, Southwest University for Nationalities, Chengdu, 610041, Sichuan, People’s Republic of China

    Ke-wei Ding

Authors
  1. Ke-wei Ding
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  2. Ming-hui Wang
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  3. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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Ding, Kw., Wang, Mh. & Huang, Nj. Distributionally robust chance constrained problem under interval distribution information. Optim Lett 12, 1315–1328 (2018). https://doi.org/10.1007/s11590-017-1160-7

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  • DOI: https://doi.org/10.1007/s11590-017-1160-7

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