Books

• Third edition: Lectures on Stochastic Programming: Modeling and Theory,  by Shapiro, A., Dentcheva, D. and Ruszczynski, A., SIAM, Philadelphia, 2021.                                                                                                         On Amazon
• Errata (third edition)
• Lectures on Stochastic Programming: Modeling and Theory, by Shapiro, A., Dentcheva, D. and Ruszczynski, A., SIAM, Philadelphia, 2009.
• Errata (first edition)
• Second edition of Lectures on Stochastic Programming: Modeling and Theory
• Errata (second edition)
• Stochastic Programming,  Handbook in Operations Research and Management Science,  edited by  Ruszczynski, A.  and Shapiro, A., Elsevier, 2003.
• Bonnans, J.F. and Shapiro, A., Perturbation Analysis of Optimization Problems, Springer, New York, 2000, Chinese edition, Science Press, 2008.
  Errata
• Rubinstein, R.Y. and Shapiro, A., Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method, John Wiley and Sons, New York, 1993.
• Shapiro, A., Topics in Stochastic Programming, CORE Lecture Series, Universite Catholique de Louvain, 2011.

Notes for class

ISyE 7401

ISyE 6402 (time series)

Reports

• Upper bound for optimal value of risk averse multistage problems, report 2016
• Report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico – January 2014
• Report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico – October 2015
• Final report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico, December 2012
• Report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico – Phase 1, April 2011
• Report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico – Risk Averse Approach, May 2011
• Report for technical cooperation between Georgia Institute of Technology and ONS – Operador Nacional do Sistema Eletrico – Time Series Model, December 2011

Preprints

• Yan Li and Alexander Shapiro, “Rectangularity and duality of distributionally robust Markov Decision Processes”, https://arxiv.org/abs/2308.11139
• Alexander Shapiro, Enlu Zhou, Yifan Lin, Yuhao Wang, “Episodic Bayesian Optimal Control with Unknown Randomness Distribution”, https://arxiv.org/abs/2308.08478
• Singh, M., Shapiro, A. and Zhang, R., “Rank one tensor completion problem”,  https://arxiv.org/abs/2009.10533
• Ding, L., Ahmed, S. and Shapiro, A., ” A Python package for multi-stage stochastic programming”, Published electronically in:  Optimization Online,   Software:  https://github.com/lingquant/msppy , YouTube Video
• Shapiro, A. and Philpott, A, “A Tutorial on Stochastic Programming “
• Nemirovski, A. and Shapiro, A., “On complexity of Shmoys – Swamy class of two-stage linear stochastic programming problems”, Published electronically in:  Optimization Online
• Shapiro, A. and Nemirovski, A., “Duality of linear conic problems”,
  Published electronically in:  Optimization Online
• Shapiro, A., “On differentiability of symmetric matrix valued functions”,
  Published electronically in:  Optimization Online
• Ahmed, S. and  Shapiro, A., “The Sample Average Approximation Method for Stochastic Programs with Integer Recourse”, Published electronically in:  Optimization Online
• Shapiro, A. and Yomdin, Y., ” On functions representable as a difference of two convex functions, and necessary conditions in a constrainted optimization”, preprint, 1981.

Parts of Books

1. Shapiro, A., “Minimum Rank Factor Analysis”, in: Encyclopedia of Statistical Sciences, pp. 532-534, Vol. 5, S. Kotz, N.L. Johnson and C.B. Read, Eds., New York, Wiley, 1985.
2. Shapiro, A., “Minimum Trace Factor Analysis”, in: Encyclopedia of Statistical Sciences, pp. 534-537, Vol. 5, S. Kotz, N.L. Johnson and C.B. Read, Eds., New York, Wiley, 1985.
3. Rubinstein, R.Y., Shapiro, A. and Uryas’ev, S., “The Score Function Method”, in: Encyclopedia of Operations Research and Management Science, Gass, S.I. and C.M. Harris, Editors, pp. 614-617, Kluwer Academic Publishers, 1996.
4. Shapiro, A., “Optimality conditions and sensitivity analysis of cone-constrained and semi-definite programs”, in: Topics in semidefinite and interior-point methods, pp. 1-15, Fields Inst. Commun., 18, Amer. Math. Soc., Providence, RI, 1998.
5. Shapiro, A., “First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems”, in: R. Reemtsen and J.-J. Rueckmann, Eds., Semi-Infinite Programming, pp. 103-133, Kluwer Academic Publishers, Boston-London-Dordrecht, 1998.
6. Shapiro, A., “Semidefinite Programming: Optimality Conditions and Stability”, Encyclopedia of Optimization, Kluwer Academic Publishers, pp 3380–3384, 2008.
7. Shapiro, A., ” Duality, optimality conditions and perturbation analysis”, in: Semidefinite Programming and Applications Handbook, R. Saigal and L. Vandenberghe and H.Wolkowicz, Eds., KluwerAcademic Publishers, Boston, pp.67-92, 2000.
8. Shapiro, A., “Statistical inference of   stochastic optimization problems”, in:  Probabilistic Constrained
   Optimization: Methodology and Applications.  Uryasev, S. (Ed.), Kluwer Academic Publishers, pp. 282-304, 2000.
9. Shapiro, A., “Monte Carlo simulation approach to stochastic programming “, in:  Proceedings of the 2001 Winter Simulation Conference, B. A. Peters, J. S. Smith, D. J. Medeiros, and M. W. Rohrer, eds.
10. Kleywegt, A.J. and Shapiro, A., “Stochastic Optimization”,  3rd Edition of the Handbook of Industrial Engineering, Gavriel Salvendy, Ed., John Wiley, New York, pp. 2625 – 2650, 2001.
11. Shapiro, A.  “On duality theory of conic linear problems”,   Miguel A. Goberna and Marco A. Lopez, Eds., Semi-Infinite Programming: Recent Advances,   Kluwer Academic Publishers, pp. 135 – 165, 2001.
12. Nemirovski, A. and Shapiro, A., “Scenario approximations of chance constraints“,
    Published electronically in:  Optimization Online
    Published in: Probabilistic and Randomized Methods for Design under Uncertainty, pp. 3-48, G. Calafiore and F. Dabbene (Eds.), Springer, London, 2005.
13. Shapiro, A. and Nemirovski, A., “On complexity of stochastic programming problems”,
    Published electronically in:  Optimization Online
    Published in: Continuous Optimization: Current Trends and Applications, pp. 111-144, V. Jeyakumar and A.M. Rubinov (Eds.), Springer, 2005.
14. Ruszczynski, A. and Shapiro, A., “Optimization of Risk Measures”,
    Published in: Probabilistic and Randomized Methods for Design under Uncertainty, G. Calafiore and F. Dabbene (Eds.), Springer, London, 2005.
15. Shapiro, A., “Statistical Inference of Moment Structures”,Handbook of Latent Variable and Related Models, Sik-Yum Lee (Ed.), Elsevier, Amsterdam, 2007.
16. Shapiro, A., “Computational Complexity of Stochastic Programming: Monte Carlo Sampling Approach”, Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010.
17. Shapiro, A., Statistical Inference of covariance structures, in Current Topics in the Theory and Application of Latent Variable Models, Edited by Michael C. Edwards and Robert C. MacCallum, pp. 198 – 216, Taylor & Francis, New York, 2013.
    https://books.google.com/books?isbn=1848729510
18. Kouri, D.P. and Shapiro, A., Optimization of PDEs with Uncertain Inputs, in Frontiers in PDE-Constrained Optimization, Edited by Antil, H., Kouri, D.P., Lacasse, M.-D., Ridzal, D., pp. 41-81, The IMA Volumes in Mathematics and its Applications, Springer, 2018.

Published Journal Papers (refereed)

1. Shapiro, A., “Rank-Reducibility of a Symmetric Matrix and Sampling Theory of Minimum Trace Factor Analysis”, Psychometrika, vol. 47, pp. 187-199, 1982.
2. Shapiro, A., “Optimally Scaled Matrices, Necessary and Sufficient Conditions”, Numerische Mathematik, vol. 39, pp. 239-245, 1982.
3. Shapiro, A., “Weighted Minimum Trace Factor Analysis”, Psychometrika, vol. 47, pp. 243-264, 1982.
4. Della Riccia, G. and Shapiro, A., “Minimum Rank and Minimum Trace of Covariance Matrices”, Psychometrika, vol. 47, pp. 443-448, 1982.
5. Shapiro, A., “On Unsolvability of Inverse Eigenvalue Problems Almost Everywhere”, Linear Algebra and Applications, vol. 49, pp. 27-31, 1983.
6. Della Riccia, G. and Shapiro, A., “Fisher Discriminant Analysis and Factor Analysis”, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-5, pp. 99-104, 1983.
7. Shapiro, A., “Asymptotic Distribution Theory in the Analysis of Covariance Structures (a unified approach)”, South African Statistical Journal, vol. 17, pp. 33-81, 1983.
8. Shapiro, A. and Browne , M.W., “On the Investigation of Local Identifiability: a Counter-Example”, Psychometrika, vol. 48, pp. 303-304, 1983.
9. Shapiro, A., “A Note on the Consistency of Estimators in the Analysis of Moment Structures”, British Journal of Mathematical and Statistical Psychology, vol. 37, pp. 84-88, 1984.
10. Shapiro, A., “On Optimality Conditions in Quasidifferentiable Optimization”, SIAM J. Control and Optimization, vol. 22, pp. 610-617, 1984.
11. Shapiro, A., “Optimal Block Diagonal l2-Scaling of Matrices”, SIAM J. Numerical Analysis, vol. 22, pp. 81-94, 1985.
12. Shapiro, A., “Asymptotic Distribution of Test Statistics in the Analysis of Moment Structures Under Inequality Constraints”, Biometrika, vol. 72, pp. 133-144, 1985.
13. Shapiro, A., “Asymptotic Equivalence of Minimum Discrepancy Function Estimators to GLS Estimators “, South African Statistical Journal, vol. 19, pp. 73-81, 1985.
14. Shapiro, A., “Extremal Problems on the Set of Nonnegative Definite Matrices”, Linear Algebra and Applications, vol. 67, pp. 7-18, 1985.
15. Shapiro, A., “A Note on the Asymptotic Distribution of the Greatest Lower Bound to Reliability”, Psychometrika, vol. 50, pp. 243-244, 1985.
16. Shapiro, A., “Identifiability of Factor Analysis, Some Results and Open Problems”, Linear Algebra and Applications, vol. 70, pp. 1-7, 1985.
17. Steiger, J.H., Shapiro, A. and Browne, M.W., “On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics”, Psychometrika, vol. 50, pp. 253-264, 1985.
18. Shapiro, A., “Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs”, Mathematics of Operations Research, vol. 10, pp. 207-219, 1985.
19. Shapiro, A., “Second-Order Sensitivity Analysis and Asymptotic Theory of Parametrized Nonlinear Programs “, Mathematical Programming, vol. 33, pp. 280-299, 1985.
20. Shapiro, A., “Asymptotic Theory of Overparametrized Structural Models”, Journal of the American Statistical Association, vol. 81, pp. 142-149, 1986.
21. Shapiro, A., “Quasidifferential Calculus and First-Order Optimality Conditions in Nonsmooth Optimization”, Mathematical Programming Studies, vol. 29, pp. 56-68, 1986.
22. Browne, M.W. and Shapiro, A., “The Asymptotic Covariance Matrix of Sample Correlation Coefficients under General Conditions”, Linear Algebra and Applications, vol. 82, pp. 169-176, 1986.
23. Shapiro, A., “On Differentiability of metric projections in R^n, 1: Boundary Case”, Proceedings of the American Mathematical Society, vol. 99, pp. 123-128, 1987.
24. Shapiro, A., “A Conjecture Related to Chi-Bar-Squared Distributions”, The American Mathematical Monthly, vol. 94, pp. 46-48, 1987 and Proofs
25. Shapiro, A., “Robustness Properties of the MDF Analysis of Moment Structures”, South African Statistical Journal, vol. 21, pp. 39-62, 1987.
26. Shapiro, A. and Browne, M.W., “Analysis of Covariance Structures Under Elliptical Distributions,” Journal of the American Statistical Association, Vol. 82, pp. 1092-1097, 1987.
27. Browne, M.W. and Shapiro, A., “Adjustments for Kurtosis in Factor Analysis with Elliptically Distributed Errors”, Journal Royal Statistical Society, Series B, vol. 49, pp. 346-352, 1987.
28. Kano, Y. and Shapiro, A., “On Asymptotic Variance of Uniqueness Estimators in Factor Analysis”, South African Statistical Journal, vol. 21, pp. 131-136, 1987.
29. Shapiro, A., “Directional Differentiability of Metric Projections Onto Moving Sets at Boundary Points”, Journal of Mathematical Analysis and Applications, vol. 131, pp. 392-403, 1988.
30. Shapiro, A., “Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis,” International Statistical Review, vol. 56, pp. 49-62, 1988.                                                                                                    Complement result about chi-bar-squared distributions
31. Shapiro, A., “Sensitivity Analysis of Nonlinear Programs and Differentiability Properties of Metric Projections”, SIAM J. Control and Optimization, vol. 26, pp. 628-645, 1988.
32. Browne, M.W. and Shapiro, A., “Robustness of Normal Theory Methods in the Analysis of Linear Latent Variate Models”, British Journal of Mathematical and Statistical Psychology, vol. 41, pp. 193-208, 1988.
33. Botha, J.D., Shapiro, A. and Steiger, J.H., “Uniform Indices of Fit for Factor Analysis Models”, Multivariate Behavioral Research, vol. 23, pp. 443-450, 1988.
34. Shapiro, A., “Perturbation Theory of Nonlinear Programs When the Set of Optimal Solutions is Not a Singleton”, Applied Mathematics & Optimization. An International Journal, vol. 18, pp. 215-229, 1988.
35. Shapiro, A. and Botha, J.D., “Dual Algorithms for Orthogonal Procrustes Rotations”, SIAM Journal on Matrix Analysis and Applications, vol. 9, pp. 378-383, 1988.
36. Shapiro, A. and Browne, M.W., “On the Asymptotic Bias of Estimators Under Parameter Drift”, Statistics and Probability Letters, vol. 7, pp. 221-224, 1989.
37. Shapiro, A., “Asymptotic Properties of Statistical Estimators in Stochastic Programming,” The Annals of Statistics, Vol. 17, pp. 841-858, 1989.
38. Shapiro, A., “On Differential Stability in Stochastic Programming”, Mathematical Programming, vol. 47, pp. 107-116, 1990.
39. Shapiro, A. and Browne, M.W., “On the Treatment of Correlation Structures as Covariance Structures”, Linear Algebra and Applications, vol. 127, pp. 567-587, 1990.
40. Shapiro, A., “On Concepts of Directional Differentiability”, Journal of Optimization Theory and Applications, vol. 66, pp. 447-487, 1990.
41. Shapiro, A. and Cohen, A., “Testing and Estimation of Equal Variances for Correlated Variables”, Statistics and Probability Letters, vol. 10, pp. 231-234, 1990.
42. Rubinstein, R.Y. and Shapiro, A., “Optimization of Static Simulation Models by the Score Function Method”, Mathematics and Computers in Simulation, vol. 32, pp. 373-392, 1990.
43. Shapiro, A. and Botha, J.D., “Variogram Fitting with a General Class of Conditionally Nonnegative Definite Functions”, Computational Statistics & Data Analysis, vol. 11, pp. 87-96, 1991.
44. Shapiro, A., “Upper Bounds for Nearly Optimal Diagonal Scaling of Matrices”, Linear and Multilinear Algebra, vol. 29, pp. 145-147, 1991.
45. Shapiro, A., “Asymptotic Analysis of Stochastic Programs”, Annals of Operations Research, vol. 30, pp. 169-186, 1991.
46. Browne, M.W. and Shapiro, A., “Invariance of Covariance Structures under Groups of Transformations”, Metrika, vol. 38, pp. 345-355, 1991.
47. Shapiro, A. and Delport, J.L., “Statistical Analysis of Jointed Rock Data”, International Journal of Rock Mechanics and Mining Sciences, vol. 28, pp. 375-382, 1991.
48. Shapiro, A., “Perturbation Analysis of Optimization Problems in Banach Spaces”, Numerical Functional Analysis and Optimization, vol. 13, pp. 97-116, 1992.
49. Shapiro, A. and Bonnans, J.F., “Sensitivity Analysis of Parametrized Programs under Cone Constraints”, SIAM J. Control and Optimization, vol. 30, pp. 1409-1422, 1992.
50. Shapiro, A., Botha, J.D., Pastore, A. and Lesk, A., “A Method for Multiple Superposition of Structures”, Acta Crystallographica, vol. A48, pp. 11-14, 1992.
51. Bonnans, J.F., Ioffe, A.D. and Shapiro, A., “Developpement de Solutions Exactes et Approchees en Programmation Non Linearire”, C.R. Acad. Sc. Paris, vol. 315, Serie I, pp. 119-123, 1992.
52. Shapiro, A. and Al-Khayyal, F., “First-Order Conditions for Isolated Locally Optimal Solutions”, Journal of Optimization Theory and Applications, vol. 77, pp. 189-196, 1993.
53. Shapiro, A., “Asymptotic Behavior of Optimal Solutions in Stochastic Programming,” Mathematics of Operations Research, vol. 18, pp. 829-845, 1993.
54. Shapiro, A., “Existence and Differentiability of Metric Projections in Hilbert Spaces”, SIAM Journal on Optimization, vol. 4, pp. 130-141, 1994.
55. Shapiro, A., “Sensitivity Analysis of Parametrized Programs via Generalized Equations”, SIAM J. Control and Optimization, vol. 32, pp. 553-571, 1994.
56. Shapiro, A. and Wardi, Y., “Nondifferentiability of the Steady-State Function in Discrete Event Dynamic Systems”, IEEE Transactions on Automatic Control, vol. 39, pp. 1707-1711, 1994.
57. Shapiro, A., “On Lipschitzian Stability of Optimal Solutions of Parametrized Semi-Infinite Programs”, Mathematics of Operations Research, vol. 19, pp. 743-752, 1994.
58. Shapiro, A., “Quantitative Stability in Stochastic Programming”, Mathematical Programming, Series A, vol. 67, pp. 99-108, 1994.
59. Shapiro, A., “Directionally Nondifferentiable Metric Projection”, Journal of Optimization Theory and Applications, vol. 81, pp. 203-204, 1994.
60. Shapiro, A. and Fan, M.K.H., “On Eigenvalue Optimization”, SIAM J. Optimization, 5, pp. 552-569, 1995.
61. Shapiro, A., “Directional Differentiability of the Optimal value Function in Convex Semi-Infinite Programming”, Mathematical Programming, Series A, 70, pp. 149-157, 1995.
62. Shapiro, A. and Wardi, Y., “Convergence Analysis of Stochastic Algorithms”, Mathematics of Operations Research, 21, pp. 615-628, 1996.
63. Shapiro, A. and Wardi, Y., “Convergence Analysis of Gradient Descent Stochastic Algorithms”, Journal of Optimization Theory and Applications, 91, pp. 439-454, 1996.
64. Rehman, S.U., and Shapiro, A., “An integral transform approach to cross-variograms modeling”, Computational Statistics and Data Analysis, 22, pp. 213-233, 1996.
65. Shapiro, A., “Simulation-based optimization – convergence analysis and statistical inference”, Commun. Statist.-Stochastic Models, 12, pp. 425-454, 1996.
66. Shapiro, A., “On Uniqueness of Lagrange Multipliers in Optimization Problems Subject to Cone Constraints”, SIAM Journal on Optimization, vol. 7, pp. 508-518, 1997.
67. Shapiro, A. “First and second order analysis of nonlinear semidefinite programs”, Mathematical Programming, Series B, vol. 77, pp. 301-320, 1997.
68. Shapiro, A. and Homem-de-Mello, T., “A Simulation-Based Approach to Stochastic Programming with Recourse”, Mathematical Programming, vol. 81, pp. 301-325, 1998.
69. Bonnans, J.F. and Shapiro, A., “Optimization problems with perturbations, A guided tour”, SIAM Review, vol. 40, pp. 228-264, 1998.
70. Bonnans, J.F. and Shapiro, A., “Nondegeneracy and quantitative stability of parameterized optimization problems with multiple solutions”, SIAM J. Optimization, vol. 8, pp. 940-946, 1998.
71. Bonnans, J.F., Cominetti, R. and Shapiro, A., “Sensitivity analysis of optimization problems under second order regular constraints”, Mathematics of Operations Research, vol. 23, pp. 806-831, 1998.
72. Ten Berge, J.M.F., Krijnen, W.P., Wansbeck, T. and Shapiro, A., “Some New Results on Correlation Preserving Factor Scores Prediction Methods”, Linear Algebra and Its Applications, vol. 289, pp. 311-318, 1999.
73. Bonnans, J.F., Cominetti, R. and Shapiro, A., “Second order optimality conditions based on parabolic second order tangent sets”, SIAM J. Optimization, vol. 9, pp. 466-492, 1999.
74. Homem-de-Mello, T., Shapiro, A. and Spearman, M.L., “Finding optimal material release times using simulation based optimization”, Management Science, vol. 45, pp. 86-102, 1999.
75. Ruckmann, J.J. and Shapiro, A., “On first order optimality conditions in generalized semi-infinite programming”, Journal Optimization Theory and Applications, vol. 101, pp. 677-691, 1999.
76. Shapiro, A. and Ten Berge, J.M.F.,  “The asymptotic bias of Minimum Trace Factor Analysis, with applications to the greatest lower bound to reliability”,   Psychometrika, vol. 65,  pp. 413-425, 2000.
77. Shapiro, A., “On the asymptotics of constrained local M-estimators”, The Annals of Statistics, vol. 28,  pp. 948-960, 2000.
78. Shapiro, A. and   Homem-de-Mello, T., “On rate of convergence of Monte Carlo approximations of stochastic programs”,
    SIAM J. Optimization, vol. 11, pp. 70-86, 2000.
79. Ruckmann, J.J. and Shapiro, A., “Second order optimality conditions in generalized semi-infinite programming”,  Set-Valued Analysis, vol. 9, pp. 169-186, 2001.
80. Kleywegt, A.J.,  Shapiro, A. and Homem-de-Mello, T.,  “The sample average approximation method for stochastic discrete optimization”, SIAM J. Optimization, vol. 12, pp. 479-502, 2001.
81. Shapiro, A. and Ten Berge, J.M.F.,  “Statistical Inference of Minimum Rank  Factor Analysis”, Psychometrika, vol. 67, pp. 79-94, 2002.
82. Doveh, E., Shapiro, A. and Feigin, P.D., “Testing of monotonicity in regression models”, Journal of Statistical Planning and Inference,  vol. 107, pp. 289-306, 2002.
83. Shapiro, A. and Kleywegt, A.J.,  “Minimax analysis of stochastic problems”,  Optimization Methods and Software, vol. 17, pp. 523-542, 2002.
84. Shapiro, A.,  Homem-de-Mello,T. and  Kim, J.C., “Conditioning of convex piecewise linear stochastic programs”, Mathematical Programming, Ser. A, vol. 94, pp. 1-19, 2002.
85. Verweij, B.,  Ahmed, S.,  Kleywegt, A.J., Nemhauser, G. and Shapiro, A.,  “The sample average approximation method applied to stochastic routing problems: a computational study”,  Computational Optimization and Applications, vol. 24, pp. 289-333, 2003.
86. Shapiro, A.,  “Sensitivity analysis of generalized equations”, Journal of Mathematical Sciences, vol. 115, pp. 2554-2565, 2003.
87. Shapiro, A.,  “Inference of statistical bounds for multistage stochastic programming problems”, Mathematical Methods of Operations Research, vol. 58, pp. 57-68, 2003.
88. Shapiro, A.,  “On a class of nonsmooth composite functions”, Mathematics of Operations Research, vol. 28, pp. 677-692, 2003.
89. Shapiro, A.,  “Scheffe’s method for constructing simultaneous confidence intervals subject to cone constraints”, Statistics and Probability Letters, vol. 64, pp.403-406, 2003.
90. Shapiro, A. and Ahmed, S.,  “On a class of minimax stochastic programs”, SIAM J. Optimization, vol. 14, pp. 1237-1249, 2004.
91. Shapiro, A. and Sun, Jie., “Some properties of the augmented Lagrangian in cone constrained optimization”, Mathematics of Operations Research, vol. 29, pp. 479-491, 2004.
92. Santoso , T., Ahmed, S., Goetschalckx, M. and Shapiro, A.,  “A stochastic programming approach for supply chain network design under uncertainty”, European Journal of Operational Research, vol. 167, pp. 96 -115, 2005.
93. Shapiro, A., “Sensitivity analysis of parameterized variational inequalities”, Mathematics of Operations Research, vol. 30, pp. 109 – 126, 2005.
94. Qi., L., Shapiro, A. and  Ling, C., “Differentiability and semismoothness properties of integral functions and their applications”, Mathematical Programming, Ser. A,   vol. 102, pp. 223 -248, 2005.
95. Shapiro, A, “On duality theory of convex semi-infinite programming”, Optimization,  vol. 54, pp. 535 – 543, 2005.
96. Shapiro, A, “On complexity of multistage stochastic programs”, Operations Research Letters,   vol. 34, pp. 1 – 8, 2006.
97. Linderoth, J., Shapiro, A., Wright, S.,  “The empirical behavior of sampling methods for stochastic programming”,  Annals of Operations Research, vol. 142, pp. 215-241, 2006.
98. Shapiro, A., “Worst-case distribution analysis of stochastic programs”, Mathematical Programming, Ser. B, vol. 107, pp. 91-96, 2006.
99. Shapiro, A., “Stochastic programming with equilibrium constraints”, Journal Optimization Theory and Applications, vol. 128, pp. 223-243, 2006.
100. Ruszczynski, A. and Shapiro, A., “Optimization of convex risk functions”,  Mathematics of Operations Research, vol. 31, pp. 433-452, 2006.
101. Ruszczynski, A. and Shapiro, A., “Conditional Risk Mappings”,   Mathematics of Operations Research, vol. 31, pp. 544-561, 2006.
102. Qian, Z. and  Shapiro, A., “Simulation-based approach to estimation of latent variable models”, Computational Statistics and Data Analysis,  vol. 51, pp. 1243-1259, 2006.
103. Blomvall, J. and Shapiro, A., “Solving Multistage Asset Investment Problems by Monte Carlo Based Optimization”,Mathematical Programming, Series B, vol. 108, pp. 571-595, 2006.
104. Nemirovski, A. and Shapiro, A., “Convex approximations of chance constrained programs”,
     SIAM J. Optimization, vol. 17, pp. 969-996, 2006.
105. Shapiro, A. and Huifu Xu, “Uniform Laws of Large Numbers for Set-Valued Mappings and Subdifferentials of Random Functions”,  Journal of Mathematical Analysis and Applications, vol. 325 , pp. 1390-1399, 2007.
106. Ahmed, S., Cakmak, U. and Shapiro, A.,”Coherent Risk Measures in Inventory Problems”,
     European Journal of Operational Research, vol. 182, pp. 226-238, 2007.
107. Trindade, A., Uryasev, S., Shapiro, A. and Zrazhevsky, G., “Financial prediction with constrained tail risk “,
     Journal of Banking and Finance, vol. 31, pp.3524-3538, 2007.
108. Shapiro, A., “Stochastic Programming Approach to Optimization under Uncertainty”,
     Mathematical Programming, Series B, vol. 112, pp. 183-220, 2008.
109. Shapiro, A., “Asymptotics of minimax stochastic programs”, Statistics and Probability Letters, vol. 78, pp. 150-157, 2008.
110. Shapiro, A. and Huifu Xu, “Stochastic Mathematical Programs with Equilibrium Constraints, Modeling and Sample Average Approximation”,  Optimization, vol. 57, pp. 395-418, 2008.
111. Ruckmann, J.J. and  Shapiro, A., “Augmented Lagrangians in semi-infinite programming”, Mathematical Programming, Series B,  vol. 116, pp. 499-512, 2009.
112. Shapiro, A., “Asymptotic normality of test statistics under alternative hypotheses”, Journal of Multivariate Analysis, vol. 100, pp. 936-945, 2009.
113. Nemirovski, A., Juditsky, A., Lan, G. and  Shapiro, A., “Robust stochastic approximation approach to stochastic programming”, SIAM J. Optimization, vol 19, pp. 1574 – 1609, 2009.
114. Shapiro, A., “Semi-infinite programming, duality, discretization and optimality conditions“, Optimization, vol. 58, pp. 133-161, 2009.
115. Pagnoncelli, B., Ahmed, S. and Shapiro, A., “Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications “, Journal Optimization Theory and Applications, vol. 142, pp. 399-416, 2009.
116. Shapiro, A. “On a time consistency concept in risk averse multi-stage stochastic programming”, Operations Research Letters, vol. 37, pp. 143-147, 2009.
117. Chun, S.Y. and Shapiro, A. “Normal versus noncentral chi-square asymptotics of misspecified models”, Multivariate Behavioral Research, vol. 44, pp. 803-827, 2009.
118. Chun, S.Y. and Shapiro, A., “Construction of covariance matrices with a specified discrepancy function minimizer, with application to factor analysis“, SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 1570-1583, 2010.
119. Shapiro, A., “Analysis of Stochastic Dual Dynamic Programming Method”, European Journal of Operational Research, vol. 209, pp. 63-72, 2011.
120. Shapiro, A., “A dynamic programming approach to adjustable robust optimization”, Operations Research Letters, vol. 39, pp. 83-87, 2011.
121. Shapiro, A., “Minimax and risk averse multistage stochastic programming”, European Journal of Operational Research, vol. 219, pp. 719-726, 2012.
122. Lan, G., Nemirovski, A. and Shapiro, A., “Validation Analysis of Robust Stochastic Approximation Method”, Mathematical Programming, Series A, vol. 134, pp. 425-458, 2012.
123. Chun, S.Y., Shapiro, A. and Uryasev, S., “Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics”, Operations Research, vol. 60, pp. 739-756, 2012.
124. Linwei Xin and Shapiro, A., “Bounds for nested law invariant coherent risk measures”, Operations Research Letters, vol. 40, pp. 431-435, 2012.
125. Shapiro, A., “Time consistency of dynamic risk measures”, Operations Research Letters, vol. 40, pp. 436-439, 2012.
126. Alexander Shapiro, Wajdi Tekaya, Joari Paulo da Costa, Murilo Pereira Soares, “Risk neutral and risk averse Stochastic Dual Dynamic Programming method”, European Journal of Operations Research, vol. 224, pp. 375-391, 2013.
127. Shapiro, A., “On Kusuoka representation of law invariant risk measures”, Mathematics of Operations Research, vol. 38, pp. 142-152, 2013.
128. Shapiro, A., “Consistency of sample estimates of risk averse stochastic programs”, Journal of Applied Probability, vol. 50, pp. 533-541, 2013.
129. Gauthier de Maere d’Aertrycke, Shapiro, A. and Smeers, Y., “Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems”, Mathematical Methods of Operations Research, vol. 77, pp. 393-405, 2013.
130. Shapiro, A., Tekaya, W., Pereira Soares, M. and Paulo da Costa, J., “Worst-case-expectation approach to optimization under uncertainty”, Operations Research, vol. 61, pp. 1435-1449, 2013.
131. Browne, M.W. and Shapiro, A., “Comments on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic”, Psychometrika, vol. 80, pp. 196-199, 2015.
132. Pichler, A. and Shapiro, A., “Minimal Representation of Insurance Prices”, Insurance: Mathematics and Economics, vol 62, pp. 184-193, 2015.
133. Bruno, S., Ahmed, S., Shapiro, A. and Street, A., “Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty”, European Journal of Operations Research, vol. 250, pp. 979-989, 2016.
134. Shapiro, A. “Rectangular sets of probability measures”, Operations Research, vol. 64, pp. 528-541, 2016.
135. Shapiro, A. “Differentiability properties of metric projections onto convex sets”, Journal of Optimization Theory and Applications, vol. 169, pp. 953-964, 2016.
136. Shapiro, A. and Ugurlu, K., “Decomposability and time consistency of risk averse multistage programs”, Operations Research Letters, vol. 44, pp. 663-665, 2016.
137. Chun, S.Y., Kleywegt, A.J. and Shapiro, A., “When Friends Become Competitors: The Design of Resource Exchange Alliances”, Management Science, vol. 63, pp. 2127 – 2145, 2017.
138. Shapiro, A., “Interchangeability principle and dynamic equations in risk averse stochastic programming”, Operations Research Letters, vol. 45, pp. 377-381, 2017.
139. Shapiro, A., “Distributionally robust stochastic programming”,SIAM J. Optimization, vol. 27(4), pp. 2258 – 2275, 2017.
140. Chun, S.Y., Browne, M.W. and Shapiro, A., “Modified Distribution-Free Goodness-of-Fit Test Statistic, Psychometrika, vol. 83, pp. 48 – 66, 2018.
141. Mafusalov, A., Shapiro, A. and Uryasev, S, “Estimation and Asymptotics for Buffered Probability of Exceedance, European Journal of Operations Research, vol. 270, pp. 826 – 836, 2018.
142. Guigues, V., Kratschmer, V. and Shapiro, A., “A Central Limit Theorem and Hypotheses Testing for Risk-averse Stochastic Programs”, SIAM Journal on Optimization, vol. 28(2), pp. 1337-1366, 2018.
143. Shapiro, A., “Statistical Inference of Semidefinite Programming”, Mathematical Programming, vol.174, pp. 77-97, 2019.
144. Lohndorf, N. and Shapiro, A., “Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming “, European Journal of Operations Research, vol. 273, pp. 650-661, 2019.
145. Chen, X., Shapiro, A. and Sun, H., “Convergence Analysis of Sample Average Approximation of Two-stage Stochastic Generalized Equations,” SIAM Journal on Optimization, vol. 29, pp.135 – 161, 2019.
146. Shapiro, A., Xie, Y. and Zhang, R., “Matrix completion with deterministic pattern: a geometric perspective”, IEEE Transactions on Signal Processing, vol. 67, pp. 1088-1103, 2019, 
147. Shapiro, A. and Xin, L., “Time inconsistency of optimal policies of distributionally robust inventory models”, Operations Research, Vol. 68, pp. 1576 – 1584, 2020.
148. Zhang, S., Eric de Sturler and Shapiro, A., “Topology Optimization with Many Right Hand Sides Using a Mirror Descent Stochastic Approximation – Reduction from Many to a Single Sample”, Journal of Applied Mechanics, Vol. 87, 2020.
149. Liu, R.P. and Shapiro, A., “Risk Neutral Reformulation Approach to Risk Averse Stochastic Programming”, European Journal of Operations Research, vol. 286, pp. 21-31, 2020.
150. Shapiro, A. and Ding, L., “Periodical Multistage Stochastic Programs”, SIAM Journal on Optimization, vol. 30, pp. 2083 – 2102, 2020.
151. Shapiro, A., “Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming”, European Journal of Operations Research, Vol. 288, pp.1-13, 2021.
152. Shapiro, A., Xie, Y. and Zhang, R., “On the Characteristic Rank for Matrix and Tensor Completion”,   IEEE Signal Processing Magazine,  Vol. 38, pp. 125 – 129,   2021.
153. Shapiro, A., Xie, Y. and Zhang, R., “Goodness-of-fit tests on manifolds”,  IEEE Transactions on Information Theory, Vol. 67, pp. 2539 – 2553, 2021. 
154. Zhang, R.,  Chen, J.,  Xie, Y.,  Shapiro, A. and  Mitra, U., “Testing Rank of Incomplete Unimodal Matrices”, IEEE Signal Processing Letters, Vol. 28, pp. 877 – 881, 2021.
155. Shapiro, A. and Cheng, Y., “Central Limit Theorem and Sample Complexity of Stationary Stochastic Programs”, Operations Research Letters, Vol. 49, pp. 676 – 681, 2021.
156. Shapiro, A., “Distributionally Robust Optimal Control and MDP Modeling”, Operations Research Letters, Vol. 49, pp. 809 – 814, 2021.
157. Pichler, A. and Shapiro, A., “Mathematical Foundations of Distributionally Robust Multistage Optimization”, SIAM Journal on Optimization, Vol.31, pp. 3044 – 3067, 2021.
158. Shapiro, A., “Distributionally Robust Modeling of Optimal Control“,   Operations Research Letters, Vol. 50, pp. 561 – 567, 2022.
159. Pichler, A., Liu, R.P. and Shapiro, A., “Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping”, Operations Research, Vol. 70, pp. 2439 – 2455, 2022. 
160. Shapiro, A. and Cheng, Y., “Dual bounds for periodical stochastic programs”, Operations Research, vol. 71, pp. 120 -128, 2023.
161. Guigues, V., Shapiro, A. and Cheng, Y., “Duality and sensitivity analysis of multistage linear stochastic programs”, European Journal of Operations  Research, Vol. 308, pp. 752 – 767, 2023.
162. Sun, H., Shapiro, A.  and Chen, X., “Distributionally Robust Stochastic Variational Inequalities”, Mathematical Programming, vol. 200, pp. 279 – 317, 2023. 
163. Guigues, V., Shapiro, A. and Cheng,Y., “Risk-Averse Stochastic Optimal Control: an efficiently computable statistical upper bound”, Operations Research Letters, Vol. 51, pp. 393 – 400, 2023.
164. Shapiro, A., “On the Differentiability of Symmetric Matrix Valued Functions”, Journal of Convex Analysis, Vol. 30 (4), pp. 1307 – 1317, 2023. 
165. Shapiro, A.,  Zhou, E. and  Lin, Y., “Bayesian Distributionally Robust Optimization”, SIAM Journal on Optimization, Vol. 33, pp. 1279 – 1304, 2023. 
166. Jose Blanchet and Alexander Shapiro, “Statistical Limit Theorems in Distributionally Robust Optimization”, Proceedings of the 2023 Winter Simulation Conference, pp. 31 – 45, 2023.
167. Guanghui Lan and Alexander Shapiro, “Numerical Methods for Convex Multistage Stochastic Optimization”, Foundations and Trends in Optimization, Vol. 6, No. 2, pp. 63 – 144, 2024.
168. Shapiro, A. and Pichler, A., “Conditional Distributionally Robust Functionals”,  Operations Research, Vol. 72, No. 6, pp. 2745–2757, 2024.  
169. Alexander Shapiro and Yan Li, “Distributionally robust stochastic optimal control”, Operations Research Letters, online.