# Alexander Shapiro

#13,798

Most Influential Person Now

Professor in H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech

## Why Is Alexander Shapiro Influential?

(Suggest an Edit or Addition)According to Wikipedia, Alexander Shapiro is an A. Russell Chandler III Chair and Professor in H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech. He was editor-in-chief of the journal Mathematical Programming, Series A and was an area editor of the journal Operations Research. Shapiro graduated with M.Sc. degree in mathematics from Moscow State University in 1971 and ten years later got his Ph.D. in applied mathematics and statistics from Ben-Gurion University of the Negev.

## Alexander Shapiro's Published Works

### Published Works

- Lectures on Stochastic Programming - Modeling and Theory (2009) (2625)
- Robust Stochastic Approximation Approach to Stochastic Programming (2008) (2080)
- The Sample Average Approximation Method for Stochastic Discrete Optimization (2002) (1635)
- Perturbation Analysis of Optimization Problems (2000) (1288)
- A stochastic programming approach for supply chain network design under uncertainty (2004) (1136)
- Convex Approximations of Chance Constrained Programs (2006) (1096)
- Monte Carlo Sampling Methods (2003) (1044)
- Optimization of Convex Risk Functions (2006) (530)
- On the multivariate asymptotic distribution of sequential Chi-square statistics (1985) (503)
- The empirical behavior of sampling methods for stochastic programming (2006) (479)
- Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications (2009) (471)
- The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study (2003) (452)
- Analysis of stochastic dual dynamic programming method (2011) (401)
- On Complexity of Stochastic Programming Problems (2005) (370)
- ON DUALITY THEORY OF CONIC LINEAR PROBLEMS (2001) (337)
- Lectures on Stochastic Programming - Modeling and Theory, Second Edition (2014) (332)
- Optimization Problems with Perturbations: A Guided Tour (1998) (325)
- Conditional Risk Mappings (2005) (303)
- A simulation-based approach to two-stage stochastic programming with recourse (1998) (297)
- On Eigenvalue Optimization (1995) (283)
- Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints (1985) (281)
- Minimax analysis of stochastic problems (2002) (261)
- Asymptotic analysis of stochastic programs (1991) (255)
- The Sample Average Approximation Method for Stochastic Programs with Integer Recourse (2002) (249)
- Risk neutral and risk averse Stochastic Dual Dynamic Programming method (2013) (248)
- On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs (2000) (237)
- Scenario Approximations of Chance Constraints (2006) (230)
- Stochastic programming approach to optimization under uncertainty (2007) (230)
- Towards a unified theory of inequality constrained testing in multivariate analysis (1988) (228)
- First and second order analysis of nonlinear semidefinite programs (1997) (211)
- Coherent risk measures in inventory problems (2007) (210)
- Simulation based optimization (1996) (204)
- On a time consistency concept in risk averse multistage stochastic programming (2009) (187)
- Robustness of normal theory methods in the analysis of linear latent variate models. (1988) (180)
- On complexity of multistage stochastic programs (2006) (178)
- Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets (1999) (177)
- Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation (2008) (164)
- Asymptotic Theory of Overparameterized Structural Models (1986) (157)
- On a Class of Minimax Stochastic Programs (2004) (154)
- Solving Chance-Constrained Stochastic Programs via Sampling and Integer Programming (2008) (147)
- A Tutorial on Stochastic Programming (2007) (147)
- Semi-infinite programming, duality, discretization and optimality conditions (2009) (146)
- Sensitivity analysis of nonlinear programs and differentiability properties of metric projections (1988) (142)
- Asymptotic Properties of Statistical Estimators in Stochastic Programming (1989) (141)
- Validation analysis of mirror descent stochastic approximation method (2012) (136)
- Optimization of Risk Measures (2006) (131)
- Risk Management with Benchmarking (2001) (122)
- Distributionally Robust Stochastic Programming (2017) (121)
- Variogram fitting with a general class of conditionally nonnegative definite functions (1991) (120)
- Analysis of Covariance Structures under Elliptical Distributions (1987) (115)
- Asymptotic distribution theory in the analysis of covariance structures (1983) (112)
- Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis (1982) (111)
- Statistical inference of minimum rank factor analysis (2002) (106)
- Asymptotic Behavior of Optimal Solutions in Stochastic Programming (1993) (105)
- Inference of statistical bounds for multistage stochastic programming problems (2003) (105)
- Stochastic programming by Monte Carlo simulation methods (2000) (95)
- Minimax and risk averse multistage stochastic programming (2012) (92)
- On Kusuoka Representation of Law Invariant Risk Measures (2013) (92)
- On concepts of directional differentiability (1990) (92)
- On rate of convergence of Monte Carlo approximations of stochastic programs (1998) (90)
- Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty (2016) (87)
- First-Order Optimality Conditions in Generalized Semi-Infinite Programming (1999) (83)
- Stochastic Approximation approach to Stochastic Programming (2013) (82)
- Existence and Differentiability of Metric Projections in Hilbert Spaces (1994) (80)
- Finding Optimal Material Release Times Using Simulation-Based Optimization (1999) (80)
- Some new results on correlation-preserving factor scores prediction methods (1999) (80)
- Convergence analysis of gradient descent stochastic algorithms (1996) (78)
- Conditioning of convex piecewise linear stochastic programs (2002) (76)
- Optimization of static simulation models by the score function method (1990) (69)
- Quantitative stability in stochastic programming (1994) (68)
- Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs (1985) (66)
- Some Properties of the Augmented Lagrangian in Cone Constrained Optimization (2004) (66)
- Perturbation analysis of optimization problems in banach spaces (1992) (65)
- Identifiability of factor analysis: Some results and open problems (1985) (65)
- Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints (1998) (65)
- Weighted minimum trace factor analysis (1982) (64)
- Financial prediction with constrained tail risk (2007) (63)
- Monte Carlo sampling approach to stochastic programming (2003) (61)
- Simulation-based optimization—convergence analysis and statistical inference (1996) (59)
- Time consistency of dynamic risk measures (2012) (58)
- Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics (2012) (57)
- Monte Carlo simulation approach to stochastic programming (2001) (56)
- Sensitivity Analysis of Generalized Equations (2003) (56)
- Stochastic Programming with Equilibrium Constraints (2006) (56)
- Duality and Optimality Conditions (2000) (55)
- Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions (2007) (55)
- Extremal Problems on the Set of Nonnegative Definite Matrices (1985) (54)
- Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs (1985) (54)
- The asymptotic covariance matrix of sample correlation coefficients under general conditions (1986) (53)
- Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton (1988) (49)
- Solving multistage asset investment problems by the sample average approximation method (2006) (48)
- Minimum rank and minimum trace of covariance matrices (1982) (48)
- On duality theory of convex semi-infinite programming (2005) (48)
- Second-Order Optimality Conditions in Generalized Semi-Infinite Programming (2001) (48)
- Convergence Analysis of Stochastic Algorithms (1996) (48)
- On Uniqueness of Lagrange Multipliers in Optimization Problems Subject to Cone Constraints (1997) (47)
- A note on the consistency of estimators in the analysis of moment structures (1984) (45)
- On the asymptotics of constrained local M-estimators (2000) (44)
- Rectangular Sets of Probability Measures (2016) (44)
- On Optimality Conditions in Quasidifferentiable Optimization (1984) (44)
- Statistical Inference of Stochastic Optimization Problems (2000) (43)
- Convergence Analysis of Sample Average Approximation of Two-Stage Stochastic Generalized Equations (2018) (42)
- Modeling time-dependent randomness in stochastic dual dynamic programming (2019) (42)
- Worst-Case-Expectation Approach to Optimization Under Uncertainty (2013) (38)
- A method for multiple superposition of structures. (1992) (38)
- The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability (2000) (37)
- A dynamic programming approach to adjustable robust optimization (2011) (37)
- Differentiability and semismoothness properties of integral functions and their applications (2005) (37)
- Computational study of a chance constrained portfolio selection problem (2008) (36)
- Worst-case distribution analysis of stochastic programs (2006) (35)
- Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming (2021) (34)
- Normal Versus Noncentral Chi-square Asymptotics of Misspecified Models (2009) (34)
- Sensitivity Analysis of Parameterized Variational Inequalities (2005) (33)
- On differential stability in stochastic programming (1990) (33)
- On a Class of Nonsmooth Composite Functions (2003) (33)
- Augmented Lagrangians in semi-infinite programming (2008) (29)
- Nondifferentiability of the steady-state function in discrete event dynamic systems (1994) (28)
- Nondegeneracy and Quantitative Stability of Parameterized Optimization Problems with Multiple Solutions (1998) (28)
- Interchangeability principle and dynamic equations in risk averse stochastic programming (2017) (27)
- Sensitivity analysis of parametrized programs under cone constraints (1992) (27)
- On Lipschitzian Stability of Optimal Solutions of Parametrized Semi-Infinite Programs (1994) (26)
- DUALITY, OPTIMALITY CONDITIONS AND PERTURBATION ANALYSIS (2000) (26)
- On the investigation of local identifiability: A counterexample (1983) (25)
- Optimality and Duality in Stochastic Programming (2003) (24)
- Directionally nondifferentiable metric projection (1994) (24)
- A Python package for multi-stage stochastic programming (2019) (24)
- Consistency of Sample Estimates of Risk Averse Stochastic Programs (2013) (22)
- Matrix Completion With Deterministic Pattern: A Geometric Perspective (2018) (21)
- Minimal representation of insurance prices (2015) (20)
- Differentiability Properties of Metric Projections onto Convex Sets (2016) (20)
- Lectures on Stochastic Programming: Modeling and Theory, Third Edition (2021) (20)
- On the treatment of correlation structures as covariance structures (1990) (20)
- Statistical Inference of Moment Structures (2007) (19)
- Bounds for nested law invariant coherent risk measures (2012) (19)
- Expansion of exact and approximate solutions in nonlinear programming (1992) (19)
- On differentiability of symmetric matrix valued functions (2002) (19)
- Mathematical Foundations of Distributionally Robust Multistage Optimization (2021) (19)
- First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems (1998) (19)
- Optimization of PDEs with Uncertain Inputs (2018) (19)
- Estimation and asymptotics for buffered probability of exceedance (2018) (18)
- Quasidifferential calculus and first-order optimality conditions in nonsmooth optimization (1986) (18)
- Directional differentiability of the optimal value function in convex semi-infinite programming (1995) (17)
- Duality of linear conic problems (2003) (17)
- Sensitivity Analysis of Parametrized Programs via Generalized Equations (1994) (16)
- Statistical analysis of jointed rock data (1991) (16)
- Uniform Indices-of-Fit for Factor Analysis Models. (1988) (16)
- Asymptotics of minimax stochastic programs (2008) (16)
- On the unsolvability of inverse eigenvalues problems almost everywhere (1983) (15)
- When Friends Become Competitors: The Design of Resource Exchange Alliances (2013) (15)
- Simulation-based approach to estimation of latent variable models (2006) (15)
- First and Second Order Analysis of Nonlinear Semideenite Programs (1997) (15)
- Adjustments for kurtosis in factor analysis with elliptically distributed errors (1987) (14)
- Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping (2018) (14)
- Directional differentiability of metric projections onto moving sets at boundary points (1988) (14)
- Uniqueness of Kusuoka Representations (2012) (14)
- Production, Manufacturing and Logistics A stochastic programming approach for supply chain network design under uncertainty (2005) (13)
- On differentiability of metric projections in ⁿ. I. Boundary case (1987) (13)
- Modified Distribution-Free Goodness-of-Fit Test Statistic (2018) (12)
- Computational Complexity of Stochastic Programming: Monte Carlo Sampling Approach (2011) (12)
- Statistical inference of multistage stochastic programming problems (2001) (12)
- Decomposability and time consistency of risk averse multistage programs (2016) (12)
- Corrigendum to: "Optimization of Convex Risk Functions, " Mathematics of Operations Research 31 (2006) 433 - 452 (2007) (11)
- Time and Dynamic Consistency of Risk Averse Stochastic Programs (2016) (11)
- First-order conditions for isolated locally optimal solutions (1993) (11)
- Optimal Block Diagonal $l_2 $-Scaling of Matrices (1985) (11)
- Second Order Necessary and Sufficient Optimality Conditions under Abstract Constraints (1996) (11)
- Technical Note - Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models (2020) (11)
- Fisher Discriminant Analysis and Factor Analysis (1983) (11)
- A Conjecture Related to Chi-Bar-Squared Distributions (1987) (10)
- Chapter 9 – Diffusion in Multicomponent Mixtures (2004) (10)
- Optimally scaled matrices, necessary and sufficient conditions (1982) (10)
- Periodical Multistage Stochastic Programs (2020) (10)
- Distributionally robust multistage inventory models with moment constraints (2013) (10)
- Risk neutral reformulation approach to risk averse stochastic programming (2019) (9)
- Invariance of covariance structures under groups of transformations (1991) (9)
- On complexity of Shmoys-Swamy class of two-stage linear stochastic programming problems (2006) (9)
- Statistical inference and hypotheses testing of risk averse stochastic programs (2016) (9)
- An integral transform approach to cross-variograms modeling (1996) (8)
- Multicomponent processes in crudes (2005) (8)
- Finite Capacity Production Planning with Random Demand and Limited Information (2000) (8)
- Asymptotic normality of test statistics under alternative hypotheses (2009) (8)
- Strategic Design of Robust Global Supply Chains: Two Case Studies from the Paper Industry (2004) (8)
- Conditioning of stochastic programs (2000) (8)
- Duality and sensitivity analysis of multistage linear stochastic programs (2019) (7)
- CHAPTER 101 Stochastic Optimization (2000) (7)
- A Central Limit Theorem and Hypotheses Testing for Risk-averse Stochastic Programs (2018) (7)
- Construction of Covariance Matrices with a Specified Discrepancy Function Minimizer, with Application to Factor Analysis (2010) (7)
- Distributionally robust Optimal Control and MDP modeling (2021) (6)
- Statistical inference of semidefinite programming (2019) (6)
- Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic (2015) (6)
- Upper bounds for nearly optimal diagonal scaling of matrices (1991) (6)
- On the asymptotic bias of estimators under parameter drift (1988) (6)
- A conjecture related to Chi-Bar-Squared (1986) (5)
- Scheffe's method for constructing simultaneous confidence intervals subject to cone constraints (2003) (5)
- Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems (2013) (5)
- Stability and Sensitivity Analysis (2000) (5)
- Dual algorithms for orthogonal Procrustes rotations (1988) (5)
- Bayesian Distributionally Robust Optimization (2021) (5)
- Upper bound for optimal value of risk averse multistage problems (2016) (4)
- Validation analysis of mirror descent stochastic approximation method (2011) (4)
- Dual Bounds for Periodical Stochastic Programs (2022) (4)
- Complexity of two and multi-stage stochastic programming problems (2005) (4)
- Final report for technical cooperation between Georgia Institute of Technology (2012) (4)
- 6. Risk Averse Optimization (2009) (4)
- Topology Optimization With Many Right-Hand Sides Using Mirror Descent Stochastic Approximation—Reduction From Many to a Single Sample (2020) (4)
- ON DIFFERENTIABILITY OF METRIC PROJECTIONS IN Rn, 1: BOUNDARY CASE (2010) (3)
- Risk-Averse Stochastic Optimal Control: an efficiently computable statistical upper bound (2021) (3)
- Guidelines for choosing parameters and for the risk averse approach (2015) (3)
- Goodness-of-Fit Tests on Manifolds (2019) (3)
- 2. Two-Stage Problems (2009) (3)
- Stationary Multistage Programs (2019) (3)
- Central limit theorem and sample complexity of stationary stochastic programs (2021) (3)
- A note on the asymptotic distribution of the greatest lower bound to reliability (1985) (3)
- Distributionally robust stochastic variational inequalities (2022) (2)
- Comments on “Quantifying Adventitious Error in a Covariance Structure as a Random Effect” by Hao Wu and Michael Browne (2015) (2)
- Strategic Design of Robust Global Supply Chains under Uncertainty (2004) (2)
- Revenue management in resource exchange seller alliances (2011) (2)
- Risk Averse Models (2011) (2)
- Investigation of the AV @ R and minimum storage energy target levels approach Final Report First activity of the technical cooperation between Georgia Institute of Technology and ONS-Operador Nacional do Sistema Elétrico (2015) (2)
- On optimal choice of reference parameters in the likelihood ratio method (1992) (2)
- Resource Exchange Seller Alliances (2013) (2)
- The Score Function (2007) (2)
- Goodness-offit tests on manifolds (2019) (1)
- ' s personal copy Financial prediction with constrained tail risk (2007) (1)
- Rank one tensor completion problem (2020) (1)
- Conditional Distributionally Robust Functionals (2022) (1)
- 5. Statistical Inference (2009) (1)
- Testing and estimation of equal variances for correlated variables (1990) (1)
- Modified Distribution-Free Goodness-of-Fit Test Statistic (2015) (1)
- Distributionally robust modeling of optimal control (2022) (1)
- Statistical Rank Selection for Incomplete Low-rank Matrices (2019) (1)
- Chapter 5: Statistical Inference (2021) (1)
- Robust analysis of stochastic problems (1999) (1)
- Chapter 7: Distributionally Robust Stochastic Programming (2021) (0)
- Change-of-Measure Approach to Risk Averse Stochastic Programming (2019) (0)
- Numerical Methods for Convex Multistage Stochastic Optimization (2023) (0)
- 1 DUALITY , OPTIMALITY CONDITIONS AND PERTURBATION ANALYSIS (2000) (0)
- Comments on: Stability in linear optimization and related topics. A personal tour (2012) (0)
- Comments on: Stability in linear optimization and related topics. A personal tour (2011) (0)
- Chapter 2: Two-Stage Problems (2021) (0)
- CONVERGENCE ANALYSIS OF SAMPLE AVERAGE 1 APPROXIMATION OF TWO-STAGE STOCHASTIC GENERALIZED (2018) (0)
- Production, Manufacturing and Logistics Coherent risk measures in inventory problems (2007) (0)
- Asymptotic Theory of Overparameterized (2007) (0)
- 8. Bibliographical Remarks (2009) (0)
- Monotone Structure in Discrete-Event Systems (P. Glasserman and D. D. Yao) (1995) (0)
- 7. Background Material (2009) (0)
- Some Mathematical Properties of Optimal Factor Analysis (1979) (0)
- Statistical Limit Theorems in Distributionally Robust Optimization (2023) (0)
- First-Order Optimally Conditions in Generalized Semi-Infinite Programming 1 (1999) (0)
- Corrections and additions for the book “ Perturbation Analysis of Optimization Problems ” (2019) (0)
- Additional Material and Applications (2000) (0)
- Statistical inference of semidefinite programming (2018) (0)
- Problem Set II : Foundations of Finance Solutions 1 Foundations of Finance Prof (0)
- On Characteristic Rank for Matrix and Tensor Completion [Lecture Notes] (2020) (0)
- Alexander Shapiro interview July 8, 1983 (1983) (0)
- Differentiability Properties of Metric Projections onto Convex Sets (2016) (0)
- Testing Rank of Incomplete Unimodal Matrices (2021) (0)
- Chapter 3: Multistage Problems (2021) (0)
- Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems (2013) (0)
- Chapter 7: Background Material (2014) (0)
- Semidefinite Programming: Optimality Conditions and Stability (2009) (0)
- On complexity ofmultistage stochastic programs (2005) (0)
- Moment Convergence Rate in Stochastic Optimization (2012) (0)
- Remarks on Factor Analysis Procedures (1979) (0)
- Henry Shapiro (2014) (0)
- 3. Multistage Problems (2009) (0)
- Chapter 1: Stochastic Programming Models (2021) (0)
- Factor Analysis and Clustering (1980) (0)
- Sensitivity Analysis of Parameterized (2005) (0)
- Multistage stochastic convex optimization (2008) (0)

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## What Schools Are Affiliated With Alexander Shapiro?

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