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Preface
Gradient estimates for Gaussian distribution functions: application to probabilistically constrained optimization problems
1. | Weierstrass Institute Berlin, Mohrenstr. 39, 10117 Berlin, Germany |
References:
[1] |
I. Deák, Subroutines for computing normal probabilities of sets - computer experiences,, Ann. Oper. Res., 100 (2000), 103.
doi: 10.1023/A:1019215116991. |
[2] |
E. De Giorgi, A. Marino and M. Tosques, Problems of evolution in metric spaces and maximal decreasing curve,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis .Mat. Natur. (8), 68 (1980), 180.
|
[3] |
M. Fabian, R. Henrion, A. Kruger and J. Outrata, Error bounds: necessary and sufficient conditions,, Set-Valued Var. Anal., 18 (2010), 121.
|
[4] |
J. Garnier, A. Omrane and Y. Rouchdy, Asymptotic formulas for the derivatives of probability functions and their monte carlo estimations,, European J. Oper. Res., 198 (2009), 848.
doi: 10.1016/j.ejor.2008.09.026. |
[5] |
A. Genz and F. Bretz, "Computation of Multivariate Mormal and Probabilities,", Lecture Notes in Statist., 195 (2009).
|
[6] |
R. Henrion and W. Römisch, Metric regularity and quantitative stability in stochastic programs with probabilistic constraints,, Math. Program., 84 (1999), 55.
|
[7] |
R. Henrion, Qualitative stability of convex programs with probabilistic constraints,, Lecture Notes in Econom. and Math. Systems, 481 (2000), 164.
|
[8] |
R. Henrion, Perturbation analysis of chance-constrained programs under variation of all constraint data,, Lecture Notes in Econom. and Math. Systems, 532 (2004), 257.
|
[9] |
R. Henrion and W. Römisch, Hölder and Lipschitz Stability of solution sets in programs with probabilistic constraints,, Math. Program., 100 (2004), 589.
doi: 10.1007/s10107-004-0507-x. |
[10] |
A. D. Ioffe, Metric regularity and subdifferential calculus,, Russian Math. Surveys, 55 (2000), 501.
doi: 10.1070/RM2000v055n03ABEH000292. |
[11] |
K. Marti, Differentiation of probability functions: the transformation method,, Comput. Math. Appl., 30 (1995), 361.
doi: 10.1016/0898-1221(95)00113-1. |
[12] |
N. Olieman and B. van Putten, Estimation method of multivariate exponential probabilities based on a simplex coordinates transform,, J. Stat. Comput. Simul., 80 (2010), 355.
doi: 10.1080/00949650802641833. |
[13] |
G. Pflug and H. Weisshaupt, Probability gradient estimation by set-valued calculus and applications in network design,, SIAM J. Optim., 15 (2005), 898.
doi: 10.1137/S1052623403431639. |
[14] |
A. Prékopa, "Stochastic Programming,", Kluwer, (1995).
|
[15] |
A. Prékopa, Probabilistic programming,, in, 10 (2003), 267.
|
[16] |
W. Römisch, Stability of stochastic programming problems,, in, 10 (2003), 483.
|
[17] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming,", MPS/SIAM Ser. Optim., 9 (2009).
|
[18] |
T. Szántai, A computer code for solution of probabilistic constrained stochastic programming problems,, in, (1988), 229.
|
[19] |
T. Szántai, Evaluation of a special multivariate gamma distribution,, Math. Program. Study, 27 (1986), 1.
doi: 10.1007/BFb0121111. |
[20] |
T. Szántai, Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function,, Ann. Oper. Res., 100 (2000), 85.
doi: 10.1023/A:1019211000153. |
[21] |
S. Uryasev, Derivatives of probability functions and some applications,, Ann. Oper. Res., 56 (1995), 287.
doi: 10.1007/BF02031712. |
show all references
References:
[1] |
I. Deák, Subroutines for computing normal probabilities of sets - computer experiences,, Ann. Oper. Res., 100 (2000), 103.
doi: 10.1023/A:1019215116991. |
[2] |
E. De Giorgi, A. Marino and M. Tosques, Problems of evolution in metric spaces and maximal decreasing curve,, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis .Mat. Natur. (8), 68 (1980), 180.
|
[3] |
M. Fabian, R. Henrion, A. Kruger and J. Outrata, Error bounds: necessary and sufficient conditions,, Set-Valued Var. Anal., 18 (2010), 121.
|
[4] |
J. Garnier, A. Omrane and Y. Rouchdy, Asymptotic formulas for the derivatives of probability functions and their monte carlo estimations,, European J. Oper. Res., 198 (2009), 848.
doi: 10.1016/j.ejor.2008.09.026. |
[5] |
A. Genz and F. Bretz, "Computation of Multivariate Mormal and Probabilities,", Lecture Notes in Statist., 195 (2009).
|
[6] |
R. Henrion and W. Römisch, Metric regularity and quantitative stability in stochastic programs with probabilistic constraints,, Math. Program., 84 (1999), 55.
|
[7] |
R. Henrion, Qualitative stability of convex programs with probabilistic constraints,, Lecture Notes in Econom. and Math. Systems, 481 (2000), 164.
|
[8] |
R. Henrion, Perturbation analysis of chance-constrained programs under variation of all constraint data,, Lecture Notes in Econom. and Math. Systems, 532 (2004), 257.
|
[9] |
R. Henrion and W. Römisch, Hölder and Lipschitz Stability of solution sets in programs with probabilistic constraints,, Math. Program., 100 (2004), 589.
doi: 10.1007/s10107-004-0507-x. |
[10] |
A. D. Ioffe, Metric regularity and subdifferential calculus,, Russian Math. Surveys, 55 (2000), 501.
doi: 10.1070/RM2000v055n03ABEH000292. |
[11] |
K. Marti, Differentiation of probability functions: the transformation method,, Comput. Math. Appl., 30 (1995), 361.
doi: 10.1016/0898-1221(95)00113-1. |
[12] |
N. Olieman and B. van Putten, Estimation method of multivariate exponential probabilities based on a simplex coordinates transform,, J. Stat. Comput. Simul., 80 (2010), 355.
doi: 10.1080/00949650802641833. |
[13] |
G. Pflug and H. Weisshaupt, Probability gradient estimation by set-valued calculus and applications in network design,, SIAM J. Optim., 15 (2005), 898.
doi: 10.1137/S1052623403431639. |
[14] |
A. Prékopa, "Stochastic Programming,", Kluwer, (1995).
|
[15] |
A. Prékopa, Probabilistic programming,, in, 10 (2003), 267.
|
[16] |
W. Römisch, Stability of stochastic programming problems,, in, 10 (2003), 483.
|
[17] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming,", MPS/SIAM Ser. Optim., 9 (2009).
|
[18] |
T. Szántai, A computer code for solution of probabilistic constrained stochastic programming problems,, in, (1988), 229.
|
[19] |
T. Szántai, Evaluation of a special multivariate gamma distribution,, Math. Program. Study, 27 (1986), 1.
doi: 10.1007/BFb0121111. |
[20] |
T. Szántai, Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function,, Ann. Oper. Res., 100 (2000), 85.
doi: 10.1023/A:1019211000153. |
[21] |
S. Uryasev, Derivatives of probability functions and some applications,, Ann. Oper. Res., 56 (1995), 287.
doi: 10.1007/BF02031712. |
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