Scenario Approximations of Chance Constraints

@inproceedings{Nemirovski2004ScenarioAO,
  title={Scenario Approximations of Chance Constraints},
  author={Arkadi Nemirovski and Alexander Shapiro},
  year={2004}
}
We consider an optimization problem of minimization of a linear function subject to the chance constraint Prob{G(x, ξ) ∈ C} ≥ 1 − ε, where C is a convex set, G(x, ξ) is bi-affine mapping and ξ is a vector of random perturbations with known distribution. When C is multi-dimensional and ε is small, like 10−6 or 10−10, this problem is, generically, a problem of minimizing under a nonconvex and difficult to compute constraint and as such is computationally intractable. We investigate the potential… CONTINUE READING
Highly Influential
This paper has highly influenced 15 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 241 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 100 extracted citations

241 Citations

0102030'06'09'12'15'18
Citations per Year
Semantic Scholar estimates that this publication has 241 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-9 of 9 references

Decision making in an uncertain environment: the scenario-based optimization approach

G. Calafiore, M. C. Campi
Working paper, • 2004
View 1 Excerpt

Monte Carlo Sampling Methods”, in A

A. Shapiro
Rusczyński and A. Shapiro, editors, Stochastic Programming, volume 10 of Handbooks in Operations Research and Management Science, North-Holland, • 2003
View 1 Excerpt

and D

A. Mülle
Stoyan, Comparison Methods for Stochastic Models and Risks, Wiley, Chichester, • 2002
View 1 Excerpt

and V

S. Boyd, L. El Ghaoui, F. Fero
Balakrishnan, Linear Matrix Inequalities in System and Control Theory – volume 15 of Studies in Applied Mathematics, SIAM, Philadelphia, • 1994
View 1 Excerpt

The Brunn-Minkowski inequality in Gauss space

C. Borell
Inventiones Mathematicae, • 1975
View 2 Excerpts