# A Sampling Method to Chance-constrained Semidefinite Optimization

### Chuan Xu, Jianqiang Cheng, Abdel Lisser

#### Abstract

Semidefinite programming has been widely studied for the last two decades. Semidefinite programs are linear programs with semidefinite constraint generally studied with deterministic data. In this paper, we deal with a stochastic semidefinte programs with chance constraints, which is a generalization of chance-constrained linear programs. Based on existing theoretical results, we develop a new sampling method to solve these chance constraints semidefinite problems. Numerical experiments are conducted to compare our results with the state-of-the-art and to show the strength of the sampling method.

#### References

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#### Paper Citation

#### in Harvard Style

Xu C., Cheng J. and Lisser A. (2015). **A Sampling Method to Chance-constrained Semidefinite Optimization** . In *Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-075-8, pages 75-81. DOI: 10.5220/0005276400750081

#### in Bibtex Style

@conference{icores15,

author={Chuan Xu and Jianqiang Cheng and Abdel Lisser},

title={A Sampling Method to Chance-constrained Semidefinite Optimization},

booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2015},

pages={75-81},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005276400750081},

isbn={978-989-758-075-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - A Sampling Method to Chance-constrained Semidefinite Optimization

SN - 978-989-758-075-8

AU - Xu C.

AU - Cheng J.

AU - Lisser A.

PY - 2015

SP - 75

EP - 81

DO - 10.5220/0005276400750081