PUBLICATIONS
Books
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.
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
Shapiro, A., Xie, Y. and Zhang, R., "Matrix completion with deterministic pattern - a geometric perspective", https://arxiv.org/pdf/1802.00047.pdf
Shapiro, A., "Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming", Published electronically
in: Optimization
Online
Chen, X., Shapiro, A. and Sun, H., "Convergence Analysis of Sample Average Approximation of Two-stage Stochastic Generalized Equations", Published electronically
in: Optimization
Online
Shapiro, A. and Xin, L., "Time inconsistency of optimal policies of distributionally robust inventory models", Published electronically
in: Optimization
Online
Shapiro, A. and Pichler, A., "Time and Dynamic Consistency of Risk Averse Stochastic Programs", Published electronically
in: Optimization
Online
Xin, L., Goldberg, D. and Shapiro, A., "Distributionally robust multistage inventory models with moment constraints", Published electronically
in: Optimization
Online
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, to appear.
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. López, 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.
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, Series B, online
144. Lohndorf, N. and Shapiro, A., "Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming ", European Journal of Operations Research, online.