[1]
|
J. R. Birge and F. Louveaux, “Introduction to Stochastic Programming,” Springer, New York, 1997.
|
[2]
|
S. W. Wallace and W. T. Ziemba, Eds., “Applications of Stochastic Programming,” Society for Industrial and Applied Mathematics, 2005.
|
[3]
|
A. J. King and R. J.-B Wets, “Epi-Convergency of Con- vex Stochastic Programs,” Stochastic and Stochastic Re- ports, Vol. 34, 1991, pp. 83-92.
|
[4]
|
A. J. King and R. T. Rockafellar, “Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Pro- gramming,” Mathematics for Operations Research, Vol. 18, No. 1, 1993, pp. 148-162. doi:10.1287/moor.18.1.148
|
[5]
|
A. Shapiro, “Asymptotic Analysis of Stochastic Programs,” Annals of Operations Resesrch, Vol. 30, No. 1, 1991, pp. 169-186. doi:10.1007/BF02204815
|
[6]
|
J. Dupacova and R. Wets, “Asymptotic Behavior of Sta- tistical Estimators and of Optimal Solutions of Stochastic Optimization Problems,” Annals of Statistics, Vol. 16, No. 4, 1988, pp. 1517-1549. doi:10.1214/aos/1176351052
|
[7]
|
T. Pennanen and M. Koivu, “Epi-Convergent Discretiza- tion of Stochastic Programs via Integration Quadratures,” Numerische Mathematik, Vol. 100, No. 1, 2005, pp. 141- 163. doi:10.1007/s00211-004-0571-4
|
[8]
|
S. A. Smolyak, “Interpolation and Quadrature Formula for the Class and ,” Doklady Akademii Nauk SSSR, Vol. 131, 1960, pp. 1028-1031. (in Russian, Eng- lish Translation: Soviet Mathematica Doklady, Vol. 4, 1963, pp. 240-243).
|
[9]
|
T. Gerstner and M. Griebel, “Numerical Integration Us- ing Sparse Grid,” Numerical Algorithms, Vol. 18, No. 3-4, 1998, pp. 209-232. doi:10.1023/A:1019129717644
|
[10]
|
M. Chen and S. Mehrotra, “Epiconvergent Scenario Gen- eration Method for Stochastic Problems via Sparse Grid,” Stochastic Programming E-Print Series, Vol. 2008, No. 7, 2008.
|
[11]
|
L. C. Evans, “Partial Differential Equations,” American Mathematical Society, Vol. 37, No. 3, 1998, pp. 363-367.
|
[12]
|
G. W. Wasilkowsi and H. Wozniakowski, “Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems,” Journal of Complexity, Vol. 11, No. 1, 1995, pp. 1-56. doi:10.1006/jcom.1995.1001
|
[13]
|
H. Brass and G. H¨ammerlin, Eds., “Bounds for Peano kernels,” Vol. 112, Birkh?user, Basel, 1993, pp. 39-55.
|
[14]
|
H. Wozniakowski, “Information-Based Complexity,” An- nual Review of Computer Science, Vol. 1, No. 1, 1986, pp. 319-380. doi:10.1146/annurev.cs.01.060186.001535
|
[15]
|
C. Roos, T. Terlaky and J.-P. Vial, “Interior Point Methods for Linear Optimization,” Springer, New York, 1997.
|
[16]
|
N. Megiddo, “Progress in Mathematical Programming, Chapter Pathways to the Optimal Set in Linear Program- ming,” Springer-Verlag, New York, 1989, p. 132.
|
[17]
|
A. V. Fiacco, “Introduction to Sensitivity and Stability Ana- lysis in Nonlinear Programming,” Academic Press, New York, 1983.
|
[18]
|
O. Güler, D. den Hertog, C. Roos and T. Terlaky, “De- generacy in Interior Point Methods for Linear Program- ming: A Survey,” Annals of Operations Research, Vol. 46-47, No. 1, 1993, pp. 107-138.
doi:10.1007/BF02096259
|
[19]
|
Y. Nesterov and A. Nemirovskii, “Interior Point Polyno- mial Algorithms in Convex Programming,” SIAM, Philadelphia, 1994.
|
[20]
|
J. Renegar, “A Mathematical View of Interior-Point Me- thods in Convex Optimization,” SIAM, Philadelphia, 2001.
|
[21]
|
S. J. Wright, “Primal-Dual Interior-Point Methods,” SIAM, Philadelphia, 1997.
|
[22]
|
W. R?misch, “An Approximation Method in Stochastic Optimal Control,” In: Optimization Techniques, Part 1, Lecture Notes in Control and Information Sciences, Sprin- ger-Verlag, New York, 1980, pp. 169-178.
|
[23]
|
H. Attouch, “Variational Convergence for Functions and Operators,” Pitman (Advanced Publishing Programs), 1984.
|
[24]
|
H. Attouch and R. J.-B. Wets, “Quantitative Stability of Variational Systems: I. The Epigraphical Distance,” Tran- sactions of the American Mathematical Society, Vol. 328, No. 2, 1991, pp. 695-729. doi:10.2307/2001800
|
[25]
|
P. Kall, “Approximation to Optimization Problems: An Elementary Review,” Mathematics of Operations Re- search, Vol. 11, No. 1, 1998, pp. 9-18.
doi:10.1287/moor.11.1.9
|
[26]
|
T.-W. Ma, “Higher Chain Formula Proved by Combina- torics,” The Electronic Journal of Combinatorics, Vol. 16, No. 21, 2009.
|