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Original Articles

Two probabilistic estimations in robust optimization

Pages 601-615 | Received 01 Apr 2006, Published online: 14 Jun 2013

References

  • Ben-Tal , A. and Nemirovski , A. 2000 . Robust solutions of linear programming problems contaminated with uncertain data . Mathematical Programming , 88 : 411 – 424 .
  • Ben-Tal , A. and Nemirovski , A. 1998 . Robust convex optimization . Mathematics of Operations Research , 23 : 769 – 805 .
  • Ben-Tal , A. and Nemirovski , A. 2002 . Robust solutions of uncertain quadratic and conic-quadratic programs . SIAM Journal on Optimization , 13 ( 2 ) : 535 – 560 .
  • Soyster , A. L. 1973 . Convex programming with set-inclusive constraints and applications to inexact linear programming . Operations Research , 21 : 1154 – 1157 .
  • Marshall , A. M. and Olkin , I. 1960 . Multivariate Chebyshcv inequalities . The Annals of Mathematical Statistics , 31 ( 4 ) : 1001 – 1014 .
  • Sun , C. R. 2005 . A comprehensive survey of robust optimization . Proceeding of the 7th Conference on Operations Research and Management . August 12–16 2005 , Nanjing . pp. 79 – 98 . in
  • Sun , C. R. On approximating D-induced polar set of a second-order cone by an ellipsoid . Journal of System Science and Complexity , submitted to
  • Calafiore and Polyak , B. 2001 . Stochastic algorithms for exact and approximate feasibility of robust LMIs . IEEE Trans. Aut. Control , 46 ( 11 ) November : 1755 – 1759 .
  • Farias , D. and Roy , B. V. Approximate dynamic programming: constraint sampling http://www.stanford.edu/class/msande339/2004notes/lecturel2.pdf
  • Bcrtsimas , D. and Sim , M. The Price of Robustness
  • Calafiore , G. and Campi , M. C. “ Uncertain convex programs: randomized solutions and confidence levels ” . In Mathematical Programming in press, Electronic version made available by Springer at D0I10.1007/sl0107-003-0499-y
  • Calafiore , G. and Campi , M. C. 2003 . Robust convex programs: randomized solutions and applications in control . Proceedings of the 42nd IEEE Conference on Decision and Control . December 2003 , Maui , Hawaii , USA. in
  • Calafiore , G. , Dabbene , F. and Tempo , R. 2000 . Randomized algorithms for probabilistic robustness with real and complex structured uncertainty . IEEE Transactions on Automatic Control , 45 ( 12 ) : 2218 – 2235 .
  • Deak , I. 1980 . “ Computation of multiple normal probabilities ” . In Recent Results in Stochastic Programming , Edited by: Kail , P. and Prekopa , A. 107 – 120 . Berlin : Springer-Verlag . in
  • Kuang , J. C. 2004 . Inequalities , Shandong Science and Technology Press .
  • EI-Ghaoui , L. and Lebret , H. 1997 . Robust solutions to least-square problems to uncertain data matrices . SIAM Journal on Matrix Analysis and Applications , 18 : 1035 – 1064 .
  • EI-Ghaoui , L. , Oustry , F. and Lebret , H. 1998 . Robust solutions to uncertain sem-definite programs . SIAM Journal on Optimization , 9 : 33 – 52 .
  • Mao , S.-S. , ed. 2003 . Statistical Handbook , 28 – 29 . Science Press .

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