Edit Profile (opens in new tab) Shapiro, Alexander Co-Author Distance Author ID: shapiro.alexander Published as: Shapiro, Alexander; Shapiro, A. Homepage: https://sites.gatech.edu/alexander-shapiro/ External Links: Wikidata · GND · IdRef · theses.fr Documents Indexed: 186 Publications since 1982, including 5 Books and 12 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Reviewing Activity: 67 Reviews Co-Authors: 70 Co-Authors with 98 Joint Publications 2,253 Co-Co-Authors all top 5 Co-Authors 78 single-authored 11 Browne, Michael W. 8 Bonnans, Joseph Frédéric 7 Ruszczyński, Andrzej 6 Ahmed, Shabbir 5 Homem-de-Mello, Tito 5 Nemirovski, Arkadi S. 5 Pichler, Alois 4 Rückmann, Jan-Joachim 3 Cheng, Yi 3 Chun, So Yeon 3 Dentcheva, Darinka 3 Guigues, Vincent 3 Kleywegt, Anton J. 3 Lan, Guanghui 3 ten Berge, Jos M. F. 3 Xie, Yao 3 Zhang, Rui 2 Botha, J. D. 2 Chen, Xiaojun 2 Cominetti, Roberto 2 Da Costa, Joari Paulo 2 Della Riccia, Giacomo 2 Ioffe, Alexander Davidovich 2 Lin, Yifan 2 Liu, Ruipeng 2 Soares, Murilo Pereira 2 Sun, Hailin 2 Tekaya, Wajdi 2 Uryasev, Stan 2 Vinnikov, Victor L. 2 Xin, Linwei 2 Xu, Huifu 2 Zhou, Enlu 1 Al-Khayyal, Faiz A. 1 Blanchet, Jose H. 1 Blomvall, Jörgen 1 Bruno, Sergio 1 Çakmak, Ulaş 1 Cohen, Ayala 1 de Maere d’Aertrycke, Gauthier 1 Ding, Lingquan 1 Doveh, E. 1 Fan, Michael Ko-Hui 1 Feigin, Paul David 1 Goetschalckx, Marc 1 Gómez, Juan Alfredo 1 Juditsky, Anatoli B. 1 Kano, Yutaka 1 Kim, Joocheol 1 Klatte, Diethard 1 Kouri, Drew P. 1 Kratschmer, Volker 1 Krijnen, Wim P. 1 Linderoth, Jeff T. 1 Ling, Chen 1 Löhndorf, Nils 1 Mafusalov, Alexander 1 Mordukhovich, Boris S. 1 Nemhauser, George L. 1 Pagnoncelli, Bernardo K. 1 Parra, Juan 1 Qi, Liqun 1 Qian, Zhiguang 1 Rehman, Salim U. 1 Rubinstein, Reuven Y. 1 Santoso, Tjendera 1 Scheinberg, Katya 1 Singh, Mohit 1 Smeers, Yves 1 Spearman, Mark L. 1 Steiger, James H. 1 Stein, Oliver 1 Street, Alexandre 1 Sun, Jie 1 Tezel, Aysun 1 Tichatschke, Rainer 1 Uǧurlu, Kerem 1 Verweij, Bram 1 Wang, Yuhao 1 Wansbeek, Tom J. 1 Weber, Gerhard-Wilhelm 1 Wright, Stephen J. all top 5 Serials 16 SIAM Journal on Optimization 15 Mathematical Programming. Series A. Series B 11 Mathematics of Operations Research 11 Operations Research Letters 11 European Journal of Operational Research 10 Psychometrika 8 Journal of Optimization Theory and Applications 6 Operations Research 6 Linear Algebra and its Applications 4 SIAM Journal on Control and Optimization 4 South African Statistical Journal 4 Statistics & Probability Letters 3 Optimization 3 Computational Statistics and Data Analysis 2 Journal of Mathematical Analysis and Applications 2 The Annals of Statistics 2 British Journal of Mathematical & Statistical Psychology 2 Journal of the American Statistical Association 2 SIAM Journal on Matrix Analysis and Applications 2 Annals of Operations Research 2 Top 2 Mathematical Methods of Operations Research 2 MOS/SIAM Series on Optimization 1 Acta Informatica 1 IEEE Transactions on Information Theory 1 Linear and Multilinear Algebra 1 Metrika 1 Applied Mathematics and Optimization 1 Biometrika 1 IEEE Transactions on Automatic Control 1 International Statistical Review 1 Journal of Applied Probability 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Management Science 1 Mathematical Programming Study 1 Mathematical Programming 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Insurance Mathematics & Economics 1 Communications in Statistics. Stochastic Models 1 IEEE Transactions on Signal Processing 1 Journal of the Royal Statistical Society. Series B 1 SIAM Review 1 IEEE Transactions on Pattern Analysis and Machine Intelligence 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Computational Optimization and Applications 1 Set-Valued Analysis 1 Journal of Mathematical Sciences (New York) 1 Journal of Convex Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Optimization Methods & Software 1 Handbooks in Operations Research and Management Science 1 MPS/SIAM Series on Optimization 1 Springer Series in Operations Research all top 5 Fields 128 Operations research, mathematical programming (90-XX) 49 Statistics (62-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 18 Numerical analysis (65-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Systems theory; control (93-XX) 6 Real functions (26-XX) 6 Probability theory and stochastic processes (60-XX) 3 Functional analysis (46-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 163 Publications have been cited 7,637 times in 4,670 Documents Cited by ▼ Year ▼ Perturbation analysis of optimization problems. Zbl 0966.49001 Bonnans, J. Frédéric; Shapiro, Alexander 1,131 2000 Lectures on stochastic programming. Modeling and theory. Zbl 1183.90005 Shapiro, Alexander; Dentcheva, Darinka; Ruszczyński, Andrzej 623 2009 Robust stochastic approximation approach to stochastic programming. Zbl 1189.90109 Nemirovski, A.; Juditsky, A.; Lan, G.; Shapiro, A. 373 2009 The sample average approximation method for stochastic discrete optimization. Zbl 0991.90090 Kleywegt, Anton J.; Shapiro, Alexander; Homem-de-Mello, Tito 341 2001 Stochastic programming. Zbl 1115.90001 289 2003 Lectures on stochastic programming. Modeling and theory. 2nd ed. Zbl 1302.90003 Shapiro, Alexander; Dentcheva, Darinka; Ruszczyński, Andrzej 264 2014 Convex approximations of chance constrained programs. Zbl 1126.90056 Nemirovski, Arkadi; Shapiro, Alexander 227 2006 A stochastic programming approach for supply chain network design under uncertainty. Zbl 1075.90010 Santoso, Tjendera; Ahmed, Shabbir; Goetschalckx, Marc; Shapiro, Alexander 180 2005 Optimization of convex risk functions. Zbl 1278.90283 Ruszczynski, Andrzej; Shapiro, Alexander 177 2006 Sample average approximation method for chance constrained programming: Theory and applications. Zbl 1175.90306 Pagnoncelli, B. K.; Ahmed, S.; Shapiro, A. 130 2009 Discrete event systems. Sensitivity analysis and stochastic optimization by the score function method. Zbl 0805.93002 Rubinstein, Reuven Y.; Shapiro, Alexander 124 1993 Analysis of stochastic dual dynamic programming method. Zbl 1208.90126 Shapiro, Alexander 118 2011 The empirical behavior of sampling methods for stochastic programming. Zbl 1122.90391 Linderoth, Jeff; Shapiro, Alexander; Wright, Stephen 111 2006 On concepts of directional differentiability. Zbl 0682.49015 Shapiro, A. 105 1990 On duality theory of conic linear problems. Zbl 1055.90088 Shapiro, Alexander 105 2001 Conditional risk mappings. Zbl 1278.90284 Ruszczynski, Andrzej; Shapiro, Alexander 98 2006 First and second order analysis of nonlinear semidefinite programs. Zbl 0888.90127 Shapiro, Alexander 89 1997 The sample average approximation method applied to stochastic routing problems: a computational study. Zbl 1094.90029 Verweij, Bram; Ahmed, Shabbir; Kleywegt, Anton J.; Nemhauser, George; Shapiro, Alexander 87 2003 Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints. Zbl 0596.62019 Shapiro, Alexander 86 1985 Risk neutral and risk averse stochastic dual dynamic programming method. Zbl 1292.90219 Shapiro, Alexander; Tekaya, Wajdi; da Costa, Joari Paulo; Soares, Murilo Pereira 84 2013 Second order optimality conditions based on parabolic second order tangent sets. Zbl 0990.90127 Bonnans, J. Frédéric; Cominetti, Roberto; Shapiro, Alexander 83 1999 On complexity of stochastic programming problems. Zbl 1115.90041 Shapiro, Alexander; Nemirovski, Arkadi 82 2005 Towards a unified theory of inequality constrained testing in multivariate analysis. Zbl 0661.62042 Shapiro, A. 82 1988 Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation. Zbl 1145.90047 Shapiro, Alexander; Xu, Huifu 81 2008 On a time consistency concept in risk averse multistage stochastic programming. Zbl 1167.90613 Shapiro, Alexander 70 2009 Asymptotic analysis of stochastic programs. Zbl 0745.90057 Shapiro, Alexander 70 1991 On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs. Zbl 0999.90023 Shapiro, Alexander; Homem-de-Mello, Tito 67 2000 Minimax analysis of stochastic problems. Zbl 1040.90030 Shapiro, Alexander; Kleywegt, Anton 64 2002 Optimization problems with perturbations: A guided tour. Zbl 0915.49021 Bonnans, J. Frédéric; Shapiro, Alexander 63 1998 A simulation-based approach to two-stage stochastic programming with recourse. Zbl 0919.90120 Shapiro, Alexander; Homem-de-Mello, Tito 62 1998 Coherent risk measures in inventory problems. Zbl 1128.90002 Ahmed, Shabbir; Çakmak, Ulaş; Shapiro, Alexander 61 2007 Scenario approximations of chance constraints. Zbl 1181.90248 Nemirovski, Arkadi; Shapiro, Alexander 58 2006 On eigenvalue optimization. Zbl 0838.90115 Shapiro, Alexander; Fan, Michael K. H. 54 1995 On a class of minimax stochastic programs. Zbl 1073.90027 Shapiro, Alexander; Ahmed, Shabbir 54 2004 Monte Carlo sampling approach to stochastic programming. Zbl 1053.90103 Shapiro, A. 51 2003 Asymptotic properties of statistical estimators in stochastic programming. Zbl 0688.62025 Shapiro, Alexander 51 1989 Asymptotic theory of overparameterized structural models. Zbl 0596.62069 Shapiro, Alexander 49 1986 Semi-infinite programming, duality, discretization and optimality conditions. Zbl 1158.90410 Shapiro, Alexander 48 2009 Stochastic programming approach to optimization under uncertainty. Zbl 1135.90033 Shapiro, Alexander 46 2008 Validation analysis of mirror descent stochastic approximation method. Zbl 1273.90154 Lan, Guanghui; Nemirovski, Arkadi; Shapiro, Alexander 44 2012 Sensitivity analysis of nonlinear programs and differentiability properties of metric projections. Zbl 0647.90089 Shapiro, Alexander 42 1988 Optimization of risk measures. Zbl 1181.90281 Ruszczyński, Andrzej; Shapiro, Alexander 42 2006 On complexity of multistage stochastic programs. Zbl 1080.90056 Shapiro, Alexander 42 2006 Inference of statistical bounds for multistage stochastic programming problems. Zbl 1116.90384 Shapiro, Alexander 40 2003 Some properties of the augmented Lagrangian in cone constrained optimization. Zbl 1082.90109 Shapiro, Alexander; Sun, Jie 40 2004 First-order optimality conditions in generalized semi-infinite programming. Zbl 0956.90055 Rückmann, J. J.; Shapiro, A. 39 1999 Distributionally robust stochastic programming. Zbl 1373.90089 Shapiro, Alexander 39 2017 Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis. Zbl 0539.62065 Shapiro, Alexander 36 1982 Variogram fitting with a general class of conditionally nonnegative definite functions. Zbl 0850.65382 Shapiro, A.; Botha, J. D. 33 1991 Existence and differentiability of metric projections in Hilbert spaces. Zbl 0793.41021 Shapiro, Alexander 31 1994 Convergence analysis of sample average approximation of two-stage stochastic generalized equations. Zbl 1410.90134 Chen, Xiaojun; Shapiro, Alexander; Sun, Hailin 31 2019 Robustness of normal theory methods in the analysis of linear latent variate models. Zbl 0718.62075 Browne, M. W.; Shapiro, A. 31 1988 Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs. Zbl 0579.90088 Shapiro, Alexander 30 1985 On Kusuoka representation of law invariant risk measures. Zbl 1291.91125 Shapiro, Alexander 29 2013 Minimax and risk averse multistage stochastic programming. Zbl 1253.90181 Shapiro, Alexander 28 2012 Asymptotic behavior of optimal solutions in stochastic programming. Zbl 0804.90101 Shapiro, Alexander 27 1993 Analysis of covariance structures under elliptical distributions. Zbl 0645.62056 Shapiro, Alexander; Browne, Michael W. 27 1987 Lectures on stochastic programming. Modeling and theory. 3rd edition. Zbl 1487.90507 Shapiro, Alexander; Dentcheva, Darinka; Ruszczynski, Andrzej 27 2021 Asymptotic distribution theory in the analysis of covariance structures. (A unified approach). Zbl 0517.62025 Shapiro, A. 27 1983 Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Zbl 1109.60030 Shapiro, Alexander; Xu, Huifu 26 2007 Sensitivity analysis of generalized equations. Zbl 1136.90482 Shapiro, A. 26 2003 Stochastic programming with equilibrium constraints. Zbl 1130.90032 Shapiro, A. 24 2006 Differentiability and semismoothness properties of integral functions and their applications. Zbl 1079.90143 Qi, Liqun; Shapiro, Alexander; Ling, Chen 24 2005 Identifiability of factor analysis: Some results and open problems. Zbl 0584.62089 Shapiro, Alexander 24 1985 Second-order optimality conditions in generalized semi-infinite programming. Zbl 0984.90056 Rückmann, Jan-J.; Shapiro, Alexander 23 2001 Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty. Zbl 1346.90636 Bruno, Sergio; Ahmed, Shabbir; Shapiro, Alexander; Street, Alexandre 23 2016 Quantitative stability in stochastic programming. Zbl 0828.90099 Shapiro, Alexander 22 1994 Rectangular sets of probability measures. Zbl 1342.90118 Shapiro, Alexander 22 2016 Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton. Zbl 0654.90083 Shapiro, Alexander 21 1988 Sensitivity analysis of parameterized variational inequalities. Zbl 1082.49015 Shapiro, Alexander 21 2005 Perturbation analysis of optimization problems in Banach spaces. Zbl 0763.49009 Shapiro, Alexander 21 1992 Conditioning of convex piecewise linear stochastic programs. Zbl 1023.90044 Shapiro, Alexander; Homem-de-Mello, Tito; Kim, Joocheol 20 2002 On optimality conditions in quasidifferentiable optimization. Zbl 0561.49014 Shapiro, Alexander 20 1984 Conditional value-at-risk and average value-at-risk: estimation and asymptotics. Zbl 1260.91121 Chun, So Yeon; Shapiro, Alexander; Uryasev, Stan 20 2012 Time consistency of dynamic risk measures. Zbl 1258.91111 Shapiro, Alexander 20 2012 Sensitivity analysis of optimization problems under second order regular constraints. Zbl 0977.90053 Bonnans, J. Frédéric; Cominetti, Roberto; Shapiro, Alexander 19 1998 On uniqueness of Lagrange multipliers in optimization problems subject to cone constraints. Zbl 0872.90086 Shapiro, Alexander 18 1997 Augmented lagrangians in semi-infinite programming. Zbl 1165.90030 Rückmann, Jan-J.; Shapiro, Alexander 18 2009 Second-order derivatives of extremal-value functions and optimality conditions for semi-infinite programs. Zbl 0569.90070 Shapiro, Alexander 18 1985 Duality and optimality conditions. Zbl 0957.90517 Shapiro, Alexander; Scheinberg, Katya 17 2000 On the asymptotics of constrained local \(M\)-estimators. Zbl 1105.62305 Shapiro, Alexander 17 2000 Modeling time-dependent randomness in stochastic dual dynamic programming. Zbl 1403.90536 Löhndorf, Nils; Shapiro, Alexander 17 2019 Extremal problems on the set of nonnegative definite matrices. Zbl 0565.90056 Shapiro, Alexander 16 1985 Minimal representation of insurance prices. Zbl 1318.91121 Pichler, Alois; Shapiro, Alexander 16 2015 Minimum rank and minimum trace of covariance matrices. Zbl 0539.62066 Della Riccia, Giacomo; Shapiro, Alexander 16 1982 Convergence analysis of stochastic algorithms. Zbl 0868.90114 Shapiro, A.; Wardi, Y. 15 1996 On duality theory of convex semi-infinite programming. Zbl 1147.90403 Shapiro, Alexander 15 2005 Weighted minimum trace factor analysis. Zbl 0544.62058 Shapiro, Alexander 15 1982 Solving multistage asset investment problems by the sample average approximation method. Zbl 1130.90373 Blomvall, Jörgen; Shapiro, Alexander 14 2006 On a class of nonsmooth composite functions. Zbl 1082.90117 Shapiro, Alexander 13 2003 Quasidifferential calculus and first-order optimality conditions in nonsmooth optimization. Zbl 0604.49012 Shapiro, Alexander 13 1986 A dynamic programming approach to adjustable robust optimization. Zbl 1218.90186 Shapiro, Alexander 13 2011 On differential stability in stochastic programming. Zbl 0705.90063 Shapiro, Alexander 13 1990 Interchangeability principle and dynamic equations in risk averse stochastic programming. Zbl 1409.90125 Shapiro, Alexander 12 2017 Some new results on correlation-preserving factor scores prediction methods. Zbl 1054.62559 ten Berge, Jos M. F.; Krijnen, Wim P.; Wansbeek, Tom; Shapiro, Alexander 12 1999 Convergence analysis of gradient descent stochastic algorithms. Zbl 0873.93084 Shapiro, A.; Wardi, Y. 12 1996 The asymptotic covariance matrix of sample correlation coefficients under general conditions. Zbl 0601.62077 Browne, M. W.; Shapiro, A. 12 1986 Optimization of PDEs with uncertain inputs. Zbl 1473.49030 Kouri, Drew P.; Shapiro, Alexander 11 2018 On the multivariate asymptotic distribution of sequential chi-square statistics. Zbl 0596.62020 Steiger, James H.; Shapiro, Alexander; Browne, Michael W. 11 1985 On differentiability of metric projections in \(R^ n\), 1: boundary case. Zbl 0613.41030 Shapiro, Alexander 11 1987 Duality and sensitivity analysis of multistage linear stochastic programs. Zbl 07709202 Guigues, Vincent; Shapiro, Alexander; Cheng, Yi 1 2023 Distributionally robust stochastic variational inequalities. Zbl 1519.90245 Sun, Hailin; Shapiro, Alexander; Chen, Xiaojun 1 2023 Bayesian distributionally robust optimization. Zbl 07711101 Shapiro, Alexander; Zhou, Enlu; Lin, Yifan 1 2023 Risk-averse stochastic programming: time consistency and optimal stopping. Zbl 1500.90037 Pichler, Alois; Liu, Rui Peng; Shapiro, Alexander 3 2022 Lectures on stochastic programming. Modeling and theory. 3rd edition. Zbl 1487.90507 Shapiro, Alexander; Dentcheva, Darinka; Ruszczynski, Andrzej 27 2021 Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming. Zbl 1487.90506 Shapiro, Alexander 10 2021 Mathematical foundations of distributionally robust multistage optimization. Zbl 1481.90242 Pichler, Alois; Shapiro, Alexander 8 2021 Distributionally robust optimal control and MDP modeling. Zbl 1525.90429 Shapiro, Alexander 2 2021 Technical note – time inconsistency of optimal policies of distributionally robust inventory models. Zbl 1455.90014 Shapiro, Alexander; Xin, Linwei 8 2020 Periodical multistage stochastic programs. Zbl 1448.90066 Shapiro, Alexander; Ding, Lingquan 5 2020 Risk neutral reformulation approach to risk averse stochastic programming. Zbl 1443.90264 Liu, Rui Peng; Shapiro, Alexander 3 2020 Convergence analysis of sample average approximation of two-stage stochastic generalized equations. Zbl 1410.90134 Chen, Xiaojun; Shapiro, Alexander; Sun, Hailin 31 2019 Modeling time-dependent randomness in stochastic dual dynamic programming. Zbl 1403.90536 Löhndorf, Nils; Shapiro, Alexander 17 2019 Statistical inference of semidefinite programming. Zbl 1416.62155 Shapiro, Alexander 4 2019 Matrix completion with deterministic pattern: a geometric perspective. Zbl 1414.15034 Shapiro, Alexander; Xie, Yao; Zhang, Rui 3 2019 Optimization of PDEs with uncertain inputs. Zbl 1473.49030 Kouri, Drew P.; Shapiro, Alexander 11 2018 Estimation and asymptotics for buffered probability of exceedance. Zbl 1403.90537 Mafusalov, Alexander; Shapiro, Alexander; Uryasev, Stan 8 2018 A central limit theorem and hypotheses testing for risk-averse stochastic programs. Zbl 1422.90032 Guigues, Vincent; Krätschmer, Volker; Shapiro, Alexander 4 2018 Modified distribution-free goodness-of-fit test statistic. Zbl 1402.62305 Chun, So Yeon; Browne, Michael W.; Shapiro, Alexander 1 2018 Distributionally robust stochastic programming. Zbl 1373.90089 Shapiro, Alexander 39 2017 Interchangeability principle and dynamic equations in risk averse stochastic programming. Zbl 1409.90125 Shapiro, Alexander 12 2017 Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty. Zbl 1346.90636 Bruno, Sergio; Ahmed, Shabbir; Shapiro, Alexander; Street, Alexandre 23 2016 Rectangular sets of probability measures. Zbl 1342.90118 Shapiro, Alexander 22 2016 Differentiability properties of metric projections onto convex sets. Zbl 1342.90192 Shapiro, Alexander 11 2016 Decomposability and time consistency of risk averse multistage programs. Zbl 1408.90215 Shapiro, A.; Ugurlu, K. 7 2016 Minimal representation of insurance prices. Zbl 1318.91121 Pichler, Alois; Shapiro, Alexander 16 2015 Comment on the asymptotics of a distribution-free goodness of fit test statistic. Zbl 1314.62269 Browne, Michael W.; Shapiro, Alexander 2 2015 Comments on “Quantifying adventitious error in a covariance structure as a random effect”. Zbl 1323.62122 Shapiro, A. 1 2015 Lectures on stochastic programming. Modeling and theory. 2nd ed. Zbl 1302.90003 Shapiro, Alexander; Dentcheva, Darinka; Ruszczyński, Andrzej 264 2014 Risk neutral and risk averse stochastic dual dynamic programming method. Zbl 1292.90219 Shapiro, Alexander; Tekaya, Wajdi; da Costa, Joari Paulo; Soares, Murilo Pereira 84 2013 On Kusuoka representation of law invariant risk measures. Zbl 1291.91125 Shapiro, Alexander 29 2013 Worst-case-expectation approach to optimization under uncertainty. Zbl 1291.90154 Shapiro, Alexander; Tekaya, Wajdi; Soares, Murilo Pereira; Da Costa, Joari Paulo 11 2013 Consistency of sample estimates of risk averse stochastic programs. Zbl 1301.62045 Shapiro, Alexander 8 2013 Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems. Zbl 1272.90040 de Maere d’Aertrycke, Gauthier; Shapiro, Alexander; Smeers, Yves 1 2013 Validation analysis of mirror descent stochastic approximation method. Zbl 1273.90154 Lan, Guanghui; Nemirovski, Arkadi; Shapiro, Alexander 44 2012 Minimax and risk averse multistage stochastic programming. Zbl 1253.90181 Shapiro, Alexander 28 2012 Conditional value-at-risk and average value-at-risk: estimation and asymptotics. Zbl 1260.91121 Chun, So Yeon; Shapiro, Alexander; Uryasev, Stan 20 2012 Time consistency of dynamic risk measures. Zbl 1258.91111 Shapiro, Alexander 20 2012 Bounds for nested law invariant coherent risk measures. Zbl 1258.91114 Xin, Linwei; Shapiro, Alexander 4 2012 Analysis of stochastic dual dynamic programming method. Zbl 1208.90126 Shapiro, Alexander 118 2011 A dynamic programming approach to adjustable robust optimization. Zbl 1218.90186 Shapiro, Alexander 13 2011 Computational complexity of stochastic programming: Monte Carlo sampling approach. Zbl 1229.90111 Shapiro, Alexander 2 2011 Construction of covariance matrices with a specified discrepancy function minimizer, with application to factor analysis. Zbl 1198.62060 Chun, So Yeon; Shapiro, A. 1 2010 Lectures on stochastic programming. Modeling and theory. Zbl 1183.90005 Shapiro, Alexander; Dentcheva, Darinka; Ruszczyński, Andrzej 623 2009 Robust stochastic approximation approach to stochastic programming. Zbl 1189.90109 Nemirovski, A.; Juditsky, A.; Lan, G.; Shapiro, A. 373 2009 Sample average approximation method for chance constrained programming: Theory and applications. Zbl 1175.90306 Pagnoncelli, B. K.; Ahmed, S.; Shapiro, A. 130 2009 On a time consistency concept in risk averse multistage stochastic programming. Zbl 1167.90613 Shapiro, Alexander 70 2009 Semi-infinite programming, duality, discretization and optimality conditions. Zbl 1158.90410 Shapiro, Alexander 48 2009 Augmented lagrangians in semi-infinite programming. Zbl 1165.90030 Rückmann, Jan-J.; Shapiro, Alexander 18 2009 Asymptotic normality of test statistics under alternative hypotheses. Zbl 1157.62038 Shapiro, Alexander 2 2009 Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation. Zbl 1145.90047 Shapiro, Alexander; Xu, Huifu 81 2008 Stochastic programming approach to optimization under uncertainty. Zbl 1135.90033 Shapiro, Alexander 46 2008 Asymptotics of minimax stochastic programs. Zbl 1171.90543 Shapiro, Alexander 4 2008 Coherent risk measures in inventory problems. Zbl 1128.90002 Ahmed, Shabbir; Çakmak, Ulaş; Shapiro, Alexander 61 2007 Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Zbl 1109.60030 Shapiro, Alexander; Xu, Huifu 26 2007 Convex approximations of chance constrained programs. Zbl 1126.90056 Nemirovski, Arkadi; Shapiro, Alexander 227 2006 Optimization of convex risk functions. Zbl 1278.90283 Ruszczynski, Andrzej; Shapiro, Alexander 177 2006 The empirical behavior of sampling methods for stochastic programming. Zbl 1122.90391 Linderoth, Jeff; Shapiro, Alexander; Wright, Stephen 111 2006 Conditional risk mappings. Zbl 1278.90284 Ruszczynski, Andrzej; Shapiro, Alexander 98 2006 Scenario approximations of chance constraints. Zbl 1181.90248 Nemirovski, Arkadi; Shapiro, Alexander 58 2006 Optimization of risk measures. Zbl 1181.90281 Ruszczyński, Andrzej; Shapiro, Alexander 42 2006 On complexity of multistage stochastic programs. Zbl 1080.90056 Shapiro, Alexander 42 2006 Stochastic programming with equilibrium constraints. Zbl 1130.90032 Shapiro, A. 24 2006 Solving multistage asset investment problems by the sample average approximation method. Zbl 1130.90373 Blomvall, Jörgen; Shapiro, Alexander 14 2006 Worst-case distribution analysis of stochastic programs. Zbl 1149.90112 Shapiro, Alexander 10 2006 On generalized semi-infinite programming. (With comments and rejoinder). Zbl 1111.90114 Rückmann, Jan-J.; Gómez, Juan Alfredo 6 2006 Simulation-based approach to estimation of latent variable models. Zbl 1157.62347 Qian, Zhiguang; Shapiro, Alexander 2 2006 A stochastic programming approach for supply chain network design under uncertainty. Zbl 1075.90010 Santoso, Tjendera; Ahmed, Shabbir; Goetschalckx, Marc; Shapiro, Alexander 180 2005 On complexity of stochastic programming problems. Zbl 1115.90041 Shapiro, Alexander; Nemirovski, Arkadi 82 2005 Differentiability and semismoothness properties of integral functions and their applications. Zbl 1079.90143 Qi, Liqun; Shapiro, Alexander; Ling, Chen 24 2005 Sensitivity analysis of parameterized variational inequalities. Zbl 1082.49015 Shapiro, Alexander 21 2005 On duality theory of convex semi-infinite programming. Zbl 1147.90403 Shapiro, Alexander 15 2005 On a class of minimax stochastic programs. Zbl 1073.90027 Shapiro, Alexander; Ahmed, Shabbir 54 2004 Some properties of the augmented Lagrangian in cone constrained optimization. Zbl 1082.90109 Shapiro, Alexander; Sun, Jie 40 2004 Stochastic programming. Zbl 1115.90001 289 2003 The sample average approximation method applied to stochastic routing problems: a computational study. Zbl 1094.90029 Verweij, Bram; Ahmed, Shabbir; Kleywegt, Anton J.; Nemhauser, George; Shapiro, Alexander 87 2003 Monte Carlo sampling approach to stochastic programming. Zbl 1053.90103 Shapiro, A. 51 2003 Inference of statistical bounds for multistage stochastic programming problems. Zbl 1116.90384 Shapiro, Alexander 40 2003 Sensitivity analysis of generalized equations. Zbl 1136.90482 Shapiro, A. 26 2003 On a class of nonsmooth composite functions. Zbl 1082.90117 Shapiro, Alexander 13 2003 Scheffe’s method for constructing simultaneous confidence intervals subject to cone constraints. Zbl 1116.62372 Shapiro, Alexander 1 2003 Minimax analysis of stochastic problems. Zbl 1040.90030 Shapiro, Alexander; Kleywegt, Anton 64 2002 Conditioning of convex piecewise linear stochastic programs. Zbl 1023.90044 Shapiro, Alexander; Homem-de-Mello, Tito; Kim, Joocheol 20 2002 Statistical inference of minimum rank factor analysis. Zbl 1297.62137 Shapiro, Alexander; ten Berge, Jos M. F. 7 2002 Testing of monotonicity in parametric regression models. Zbl 1015.62014 Doveh, E.; Shapiro, A.; Feigin, P. D. 3 2002 The sample average approximation method for stochastic discrete optimization. Zbl 0991.90090 Kleywegt, Anton J.; Shapiro, Alexander; Homem-de-Mello, Tito 341 2001 On duality theory of conic linear problems. Zbl 1055.90088 Shapiro, Alexander 105 2001 Second-order optimality conditions in generalized semi-infinite programming. Zbl 0984.90056 Rückmann, Jan-J.; Shapiro, Alexander 23 2001 Perturbation analysis of optimization problems. Zbl 0966.49001 Bonnans, J. Frédéric; Shapiro, Alexander 1,131 2000 On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs. Zbl 0999.90023 Shapiro, Alexander; Homem-de-Mello, Tito 67 2000 Duality and optimality conditions. Zbl 0957.90517 Shapiro, Alexander; Scheinberg, Katya 17 2000 On the asymptotics of constrained local \(M\)-estimators. Zbl 1105.62305 Shapiro, Alexander 17 2000 The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability. Zbl 1291.62245 Shapiro, Alexander; ten Berge, Jos M. F. 8 2000 Statistical inference of stochastic optimization problems. Zbl 0979.90096 Shapiro, Alexander 7 2000 Second order optimality conditions based on parabolic second order tangent sets. Zbl 0990.90127 Bonnans, J. Frédéric; Cominetti, Roberto; Shapiro, Alexander 83 1999 First-order optimality conditions in generalized semi-infinite programming. Zbl 0956.90055 Rückmann, J. J.; Shapiro, A. 39 1999 Some new results on correlation-preserving factor scores prediction methods. Zbl 1054.62559 ten Berge, Jos M. F.; Krijnen, Wim P.; Wansbeek, Tom; Shapiro, Alexander 12 1999 Finding optimal material release times using simulation-based optimization. Zbl 1231.91275 Homem-De-Mello, Tito; Shapiro, Alexander; Spearman, Mark L. 9 1999 Optimization problems with perturbations: A guided tour. Zbl 0915.49021 Bonnans, J. Frédéric; Shapiro, Alexander 63 1998 A simulation-based approach to two-stage stochastic programming with recourse. Zbl 0919.90120 Shapiro, Alexander; Homem-de-Mello, Tito 62 1998 ...and 63 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,058 Authors 84 Shapiro, Alexander 70 Zhang, Liwei 46 Xu, Huifu 43 Mordukhovich, Boris S. 31 Ahmed, Shabbir 30 Ruszczyński, Andrzej 28 Bonnans, Joseph Frédéric 28 Kuhn, Daniel 27 Chen, Zhiping 25 Van Ackooij, Wim 24 Li, Shengjie 24 Pichler, Alois 24 Qi, Liqun 23 Bentler, Peter M. 23 Lan, Guanghui 22 Sun, Hailin 22 Yao, Jen-Chih 21 Dentcheva, Darinka 21 Guigues, Vincent 21 Izmailov, Alekseĭ F. 20 Royset, Johannes O. 20 Shanbhag, Uday V. 20 Yang, Xiaoqi 19 Escudero, Laureano Fernando 19 Mehlitz, Patrick 19 Sun, Jie 19 Surowiec, Thomas 19 Wachsmuth, Gerd 18 Henrion, René 18 Hintermüller, Michael 18 Homem-de-Mello, Tito 18 Sun, Defeng 17 Jiang, Jie 17 Pang, Jong-Shi 17 Pérez-Aros, Pedro 17 Solodov, Mikhail V. 17 Nguyen Dong Yen 16 Haeser, Gabriel 16 Lin, Guihua 16 Pang, Liping 16 Yuan, Kehai 16 Zhang, Jie 16 Zhou, Jinchuan 15 Arutyunov, Aram Vladimirovic 15 Chen, Xiaojun 15 Kostyukova, Olga Ivanova 15 Pagnoncelli, Bernardo K. 15 Pflug, Georg Ch. 15 Römisch, Werner 15 Sagastizábal, Claudia A. 15 Zegeye, Habtu 15 Zhang, Jin 14 Bertsimas, Dimitris John 14 Dempe, Stephan 14 Gasnikov, Aleksandr V. 14 Kouri, Drew P. 14 Li, Guoyin 14 Liu, Yongchao 14 Maggioni, Francesca 14 Malick, Jérôme 14 Sarabi, M. Ebrahim 14 Shen, Siqian 14 Xiao, Xiantao 13 Bayraksan, Güzin 13 Branda, Martin 13 Christof, Constantin 13 Gfrerer, Helmut 13 Guo, Shaoyan 13 Liu, Jia 13 Outrata, Jiří V. 13 Schultz, Rüdiger 13 Sen, Suvrajeet 13 Tchemisova, Tatiana V. 13 Teo, Kok Lay 13 Xie, Weijun 12 de Oliveira, Welington Luis 12 Dupačová, Jitka 12 Fu, Michael C. 12 Gendreau, Michel 12 Kanzow, Christian 12 López-Cerdá, Marco Antonio 12 Mehrotra, Sanjay 12 Nemirovski, Arkadi S. 12 Norkin, Vladimir I. 12 Rockafellar, Ralph Tyrrell 12 Ye, Jane J. 12 Zhang, Dali 11 Browne, Michael W. 11 Dolgopolik, Maxim Vladimirovich 11 Fukushima, Masao 11 Huang, Ming 11 Jeyakumar, Vaithilingam 11 Lisser, Abdel 11 Luedtke, James R. 11 Morton, David P. 11 Phan Quôc Khánh 11 Song, Wen 11 Song, Yongjia 11 Thai Doan Chuong 11 Toh, Kim Chuan ...and 5,958 more Authors all top 5 Cited in 435 Serials 375 European Journal of Operational Research 352 Mathematical Programming. Series A. 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English Series 7 Machine Learning 7 Methodology and Computing in Applied Probability 7 Numerical Algebra, Control and Optimization 7 INFOR: Information Systems and Operational Research ...and 335 more Serials all top 5 Cited in 53 Fields 3,275 Operations research, mathematical programming (90-XX) 913 Calculus of variations and optimal control; optimization (49-XX) 714 Statistics (62-XX) 655 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 638 Numerical analysis (65-XX) 242 Systems theory; control (93-XX) 231 Computer science (68-XX) 227 Probability theory and stochastic processes (60-XX) 180 Operator theory (47-XX) 136 Partial differential equations (35-XX) 96 Functional analysis (46-XX) 84 Real functions (26-XX) 62 Linear and multilinear algebra; matrix theory (15-XX) 48 Global analysis, analysis on manifolds (58-XX) 45 Convex and discrete geometry (52-XX) 45 Biology and other natural sciences (92-XX) 40 Mechanics of deformable solids (74-XX) 32 Information and communication theory, circuits (94-XX) 27 Ordinary differential equations (34-XX) 23 General topology (54-XX) 22 Approximations and expansions (41-XX) 17 Measure and integration (28-XX) 15 Algebraic geometry (14-XX) 15 Fluid mechanics (76-XX) 14 Geophysics (86-XX) 9 Quantum theory (81-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Optics, electromagnetic theory (78-XX) 6 History and biography (01-XX) 5 Combinatorics (05-XX) 5 Number theory (11-XX) 4 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Difference and functional equations (39-XX) 4 Differential geometry (53-XX) 4 Manifolds and cell complexes (57-XX) 4 Mathematics education (97-XX) 3 Commutative algebra (13-XX) 3 Integral equations (45-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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