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Continuity and stability of two-stage stochastic programs with quadratic continuous recourse
1. | Department of Computing Science, School of Mathematics and Statistics, Xi'an Jiaotong University, 710049 Xi'an, Shanxi, China |
2. | School of Science, Xi'an Polytechnic University,710048 Xi'an, Shanxi, China |
References:
[1] |
B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer, Non-Linear Parametric Optimization,, Akademie Verlag, (1982). Google Scholar |
[2] |
J. R. Birge and F. Louveaux, Introduction to Stochastic Programming,, Springer, (1997).
|
[3] |
X. Chen, L. Qi and R. S. Womersley, Newton's method for quadratic stochastic programs with recourse,, J. Comput. Appl. Math., 60 (1995), 29.
doi: 10.1016/0377-0427(94)00082-C. |
[4] |
X. Chen and R. S. Womersley, Random test problems and parallel methods for quadratic programs and quadratic stochastic programs,, Optim. Method Softw., 13 (2000), 275.
doi: 10.1080/10556780008805789. |
[5] |
G. M. Cho, Log-barrier method for two-stage quadratic stochastic programming,, Appl. Math. Comput., 164 (2005), 45.
doi: 10.1016/j.amc.2004.04.095. |
[6] |
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications,, Springer-Verlag, (1998).
doi: 10.1007/978-1-4612-5320-4. |
[7] |
M. A. Goberna, M. A. López, Linear Semi-Infinite Optimization,, John Wiley and sons, (1998).
|
[8] |
Y. Han and Z. Chen, Quantitative stability of full random two-stage stochastic programs with recourse,, Optim. Lett., ().
|
[9] |
P. Kall and S. W. Wallace, Stochastic Programming,, John Wiley and Sons, (1994).
|
[10] |
W. K. Klein Haneveld and M. H. Van der Vlerk, Stochastic integer programming: general models and algorithms,, Ann. Oper. Res., 85 (1999), 39.
doi: 10.1023/A:1018930113099. |
[11] |
O. L. Mangasarian and T. H. Shiau, Lipschitz continuity of solutions of linear inequalities, programs, and complementary problems,, SIAM J. Control Optim., 25 (1987), 583.
doi: 10.1137/0325033. |
[12] |
S. Mehrotra and M. G. Özevin, Decomposition-based interior point methods for two-stage stochastic convex quadratic programs with recourse,, Oper. Res., 57 (2009), 964.
doi: 10.1287/opre.1080.0659. |
[13] |
E. L. Plambeck, B. R. Fu, S. M. Robinson and R. Suri, Sample-path optimization of convex stochastic performances functions,, Math. Program., 75 (1996), 137.
doi: 10.1016/S0025-5610(96)00010-X. |
[14] |
A. Prekopa, Stochastic Programming,, Kluwer Academic Publishers, (1995).
doi: 10.1007/978-94-017-3087-7. |
[15] |
L. Qi and R. S. Womersley, An SQP algorithm for extended linear-quadratic problems in stochastic programming,, Ann. Oper. Res., 56 (1995), 251.
doi: 10.1007/BF02031711. |
[16] |
S. T. Rachev, W. Römisch, Quantitative stability in stochastic programming: the methods of probability metrics,, Math. Oper. Res., 27 (2002), 792.
doi: 10.1287/moor.27.4.792.304. |
[17] |
S. M. Robinson, Analysis of sample-path optimization,, Math. Oper. Res., 21 (1996), 513.
doi: 10.1287/moor.21.3.513. |
[18] |
R. T. Rockafeller and R.J-B. Wets, A lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming,, Math. Program. study, 28 (1986), 63.
|
[19] |
R. T. Rockafeller and R. J-B. Wets, Variational Analysis,, Springer, (1998).
doi: 10.1007/978-3-642-02431-3. |
[20] |
W. Römisch, Stability of stochastic programming,, in Stochastic Programming: Handbooks in Operations Research and Management Science Vol.10 (eds. A. Rusczyński, (2003), 483.
doi: 10.1016/S0927-0507(03)10008-4. |
[21] |
W. Römisch and R. Schultz, Distribution sensitivity in stochastic programming,, Math. Program., 50 (1991), 197.
doi: 10.1007/BF01594935. |
[22] |
W. Römisch and R. Schultz, Lipschitz stability for stochastic programs with complete recourse,, SIAM J. Optim., 6 (1996), 531.
doi: 10.1137/0806028. |
[23] |
W. Römisch and R. J.-B. Wets, Stability of ε-approximate solutions to convex stochastic programs,, SIAM J. Optim., 18 (2007), 961.
doi: 10.1137/060657716. |
[24] |
A. Shapiro, Monte Carlo sampling methods,, in Stochastic Programming: Handbooks in Operations Research and Management Science Vol.10 (eds. A. Rusczyński, (2003), 353.
doi: 10.1016/S0927-0507(03)10006-0. |
[25] |
A. Shapiro and T. Homem-de-Mello, On rate of convergence of Monte Carlo approximations of stochastic programs,, SIAM J. Optim., 6 (1996), 531.
|
[26] |
A. Shapiro, Complexity of two and multi-stage stochastic programming problems,, 2005. Available from: , (). Google Scholar |
show all references
References:
[1] |
B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer, Non-Linear Parametric Optimization,, Akademie Verlag, (1982). Google Scholar |
[2] |
J. R. Birge and F. Louveaux, Introduction to Stochastic Programming,, Springer, (1997).
|
[3] |
X. Chen, L. Qi and R. S. Womersley, Newton's method for quadratic stochastic programs with recourse,, J. Comput. Appl. Math., 60 (1995), 29.
doi: 10.1016/0377-0427(94)00082-C. |
[4] |
X. Chen and R. S. Womersley, Random test problems and parallel methods for quadratic programs and quadratic stochastic programs,, Optim. Method Softw., 13 (2000), 275.
doi: 10.1080/10556780008805789. |
[5] |
G. M. Cho, Log-barrier method for two-stage quadratic stochastic programming,, Appl. Math. Comput., 164 (2005), 45.
doi: 10.1016/j.amc.2004.04.095. |
[6] |
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications,, Springer-Verlag, (1998).
doi: 10.1007/978-1-4612-5320-4. |
[7] |
M. A. Goberna, M. A. López, Linear Semi-Infinite Optimization,, John Wiley and sons, (1998).
|
[8] |
Y. Han and Z. Chen, Quantitative stability of full random two-stage stochastic programs with recourse,, Optim. Lett., ().
|
[9] |
P. Kall and S. W. Wallace, Stochastic Programming,, John Wiley and Sons, (1994).
|
[10] |
W. K. Klein Haneveld and M. H. Van der Vlerk, Stochastic integer programming: general models and algorithms,, Ann. Oper. Res., 85 (1999), 39.
doi: 10.1023/A:1018930113099. |
[11] |
O. L. Mangasarian and T. H. Shiau, Lipschitz continuity of solutions of linear inequalities, programs, and complementary problems,, SIAM J. Control Optim., 25 (1987), 583.
doi: 10.1137/0325033. |
[12] |
S. Mehrotra and M. G. Özevin, Decomposition-based interior point methods for two-stage stochastic convex quadratic programs with recourse,, Oper. Res., 57 (2009), 964.
doi: 10.1287/opre.1080.0659. |
[13] |
E. L. Plambeck, B. R. Fu, S. M. Robinson and R. Suri, Sample-path optimization of convex stochastic performances functions,, Math. Program., 75 (1996), 137.
doi: 10.1016/S0025-5610(96)00010-X. |
[14] |
A. Prekopa, Stochastic Programming,, Kluwer Academic Publishers, (1995).
doi: 10.1007/978-94-017-3087-7. |
[15] |
L. Qi and R. S. Womersley, An SQP algorithm for extended linear-quadratic problems in stochastic programming,, Ann. Oper. Res., 56 (1995), 251.
doi: 10.1007/BF02031711. |
[16] |
S. T. Rachev, W. Römisch, Quantitative stability in stochastic programming: the methods of probability metrics,, Math. Oper. Res., 27 (2002), 792.
doi: 10.1287/moor.27.4.792.304. |
[17] |
S. M. Robinson, Analysis of sample-path optimization,, Math. Oper. Res., 21 (1996), 513.
doi: 10.1287/moor.21.3.513. |
[18] |
R. T. Rockafeller and R.J-B. Wets, A lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming,, Math. Program. study, 28 (1986), 63.
|
[19] |
R. T. Rockafeller and R. J-B. Wets, Variational Analysis,, Springer, (1998).
doi: 10.1007/978-3-642-02431-3. |
[20] |
W. Römisch, Stability of stochastic programming,, in Stochastic Programming: Handbooks in Operations Research and Management Science Vol.10 (eds. A. Rusczyński, (2003), 483.
doi: 10.1016/S0927-0507(03)10008-4. |
[21] |
W. Römisch and R. Schultz, Distribution sensitivity in stochastic programming,, Math. Program., 50 (1991), 197.
doi: 10.1007/BF01594935. |
[22] |
W. Römisch and R. Schultz, Lipschitz stability for stochastic programs with complete recourse,, SIAM J. Optim., 6 (1996), 531.
doi: 10.1137/0806028. |
[23] |
W. Römisch and R. J.-B. Wets, Stability of ε-approximate solutions to convex stochastic programs,, SIAM J. Optim., 18 (2007), 961.
doi: 10.1137/060657716. |
[24] |
A. Shapiro, Monte Carlo sampling methods,, in Stochastic Programming: Handbooks in Operations Research and Management Science Vol.10 (eds. A. Rusczyński, (2003), 353.
doi: 10.1016/S0927-0507(03)10006-0. |
[25] |
A. Shapiro and T. Homem-de-Mello, On rate of convergence of Monte Carlo approximations of stochastic programs,, SIAM J. Optim., 6 (1996), 531.
|
[26] |
A. Shapiro, Complexity of two and multi-stage stochastic programming problems,, 2005. Available from: , (). Google Scholar |
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