• Optimization with Marginals and Moments. Author: Karthik Natarajan. Publisher: Dynamic Ideas LLC, Belmont, Massachusetts. The book is a graduate level research monograph and will be published in end 2021- early 2022


  • Distributionally robust optimization through the lens of submodularity (with Divya Padmanabhan and Arjun Ramachandra) [PDF]
  • Submodularity and Pairwise Independence (with Arjun Ramachandra) [PDF]
  • A Nonparametric Approach with Marginals for Modeling Consumer Choice (previously titled The Limit of the Marginal Distribution Model in Consumer Choice) (with Yanqiu Ruan, Li Xiaobo and Karthyek Murthy). Accepted in Twenty-Fourth ACM Conference on Economics and Computation (EC’23) [Journal Version] [Conference Version] [APPENDIX]
  • Robustness to Dependency in Influence Maximization [PDF] (Journal Version – a preliminary conference version appeared in NeurIPS 2020) (with Louis Chen, Lim Chee Chin and Divya Padmanabhan)

Accepted & Published Papers/Chapters


  • Probability Bounds for Dependent Random Events with Independent Subsets (with Arjun Ramachandra and Colin Tan) – To appear in Operations Research Letters [PDF]
  • Discrete Optimal Transport with Independent Marginals is #P-Hard (with Bahar Taşkesen, Soroosh Shafieezadeh-Abadeh and Daniel Kuhn) To appear in SIAM Journal on Optimization [PDF] [Slides]
  • Tight Probability Bounds with Pairwise Independence (with Arjun Ramachandra) To appear in SIAM Journal on Discrete Mathematics [PDF] [Video]


  • Extremal Probability Bounds in Combinatorial Optimization (with Divya Padmanabhan, Selin Damla Ahipasaoglu and Arjun Ramachandra) SIAM Journal on Optimization, 32(4): 2828-2858 [PDF] 
  • The Random QUBO. Book chapter. The Quadratic Unconstrained Binary Optimization Problem: Theory, Algorithms, and Applications, edited by A. Punnen, Springer 2022.
  • Distributionally Robust Linear and Discrete Optimization with Marginals (with Louis Chen, Will Ma, David Simchi-Levi and Zhenzhen Yan) Operations Research, 70(3): 1822–1834 [PDF]
  • A Representative Consumer Model in Data-Driven Multi-Product Pricing Optimization (with Zhenzhen Yan, Cong Cheng and Teo Chung-Piaw) Management Science, 68(8) (2022): 5798–5827 [PDF]


  • On the Heavy-Tail Behavior of the Distributionally Robust Newsvendor (with Bikramjit Das and Anulekha Dhara) Operations Research, 69(4) (2021): 1077-1099 [PDF] [Slides]
  • Exploiting Partial Correlations in Distributionally Robust Optimization (with Divya Padmanabhan and Karthyek Murthy) Mathematical Programming, 186 (2021): 209-255 [PDF]
  • Worst-Case Expected Shortfall with Univariate and Bivariate Marginals (with Anulekha Dhara and Bikramjit Das) INFORMS Journal on Computing, 33 (1), (2021): 370-389 [PDF]
  • Tree Bounds for Sums of Bernoulli Random Variables: A Linear Optimization Approach (with Divya Padmanabhan) INFORMS Journal on Optimization, 3 (1), (2021): 23- 45 [PDF] [OnlineCompanion]


  • Correlation Robust Influence Maximization (with Louis Chen, Divya Padmanabhan and Lim Chee Chin) Proceedings of the Thirty-Fourth Conference on Neural Information Processing Systems (NeurIPS 2020), Virtual-only Conference, Dec 6-12, 2020 [Link to paper] [Link to code]


  • Distributionally Robust Markovian Traffic Equilibrium (with Ugur Arikan and Selin Damla Ahipasaoglu) Transportation Science, 53 (6), (2019): 1546-1562 [PDF] 
  • Distributionally Robust Project Crashing with Partial or No Correlation Information (with Selin Damla Ahipasaoglu and Shi Dongjian), Networks, 74 (1), (2019): 79-106 [PDF]
  • A Convex Optimization Approach for Computing Correlated Choice Probabilities with Many Alternatives (with Selin Damla Ahipasaoglu and Li Xiaobo), IEEE Transactions on Automatic Control, 64 (1), (2019): 190-205 [PREZI Presentation] [FinalCode] [PDF]


  • Allocating Students to Multidisciplinary Capstone Projects Using Discrete Optimization (with Thomas Magnanti), Interfaces (Now INFORMS Journal on Applied Analytics), 48 (3) (2018): 204-216 [PDF]
  • Bounds on Random Binary Quadratic Programs (with Shi Dongjian and Toh Kim Chuan) SIAM Journal on Optimization, 28 (1) (2018): 671–692 [PDF]
  • Asymmetry and Ambiguity in Newsvendor Models (with Melvyn Sim and Joline Uichanco) Management Science, 64 (7) (2018): 3146-3167 [PDF]


  • On the Polynomial Solvability of Distributionally Robust k-Sum Optimization (with Anulekha Dhara) Optimization Methods and Software, 32 (4) (2017): 738-753, [PDF]
  • On Reduced Semidefinite Programs for Second Order Moment Bounds with Applications (with Teo Chung-Piaw) Mathematical Programming, 161 (2017): 487-518 [PDF] [Supplemental Material]


  • Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty (with Zhichao Zheng and Teo Chung-Piaw), Operations Research, 64 (6) (2016): 1406-1421 [PDF]
  • On the Flexibility of using Marginal Distribution Choice Models in Traffic Equilibrium (with Selin Damla Ahipasaoglu and Ugur Arikan) Transportation Research Part B, 91 (2016): 130-158 [PDF]


  • Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals (with Xuan Vinh Doan and Li Xiaobo) Operations Research 63, no. 6 (2015):1468-1488. [PDF]
  • Beyond Normality: A Cross Moment-Stochastic User Equilibrium Model (with Selin Damla Ahipasaoglu, Rudabeh Meskarian and Thomas Magnanti) Transportation Research Part B, Special Issue on Optimization of Urban Transportation Service Networks 81, no. 2 (2015): 333–354 [PDF] [PREZI Presentation] [MATLAB codes]


  • On Theoretical and Empirical Aspects of Marginal Distribution Choice Models (with Vinit Kumar Mishra, Dhanesh Padmanabhan, Teo Chung-Piaw and Li Xiaobo). Management Science, Special Issue on Business Analytics 60 no. 6, (2014): 1511-1531 [PDF] [PREZI Presentation]
  • A Probabilistic Model for Minmax Regret in Combinatorial Optimization (with Shi Dongjian and Toh Kim Chuan). Operations Research 62, no. 1 (2014): 160-181 [PDF]
  • Distributionally Robust Mixed Integer Linear Programs: Persistency Models with Applications (with Li Xiaobo, Zheng Zhichao and Teo Chung-Piaw) Invited Review. European Journal of Operational Research 233, no. 3, (2014): 459-473 [PDF] [Prezi Presentation]


  • New Analytical Bounds on the Average Undershoot in an Infinite Horizon (s,S) Inventory System (with Chiu Chun-Hung and Zachary Leung) Operations Research Letters 41, no. 1 (2013): 67-73 [PDF]
  • From Boxes to Bees: Active Learning in Freshmen Calculus (with F.S. Tsai, S. D. Ahipasaoglu, C. Yuen, H. Lee, N.-M. Cheung, J. Ruths, S. Huang, and T. L. Magnanti) IEEE Annual Global Engineering Education Conference (EDUCON) , 2013.


  • Choice Prediction with Semidefinite Optimization when the Utilities are Correlated (with Vinit Kumar Mishra, Tao Hua and Teo Chung-Piaw) IEEE Transactions on Automatic Control, 57, no. 10 (2012): 2450-2463 [PDF]
  • On the Complexity of Non-Overlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization (with Xuan Vinh Doan) Operations Research, 60, no. 1 (2012): 138-149 [PDF]


  • Mixed Zero-One Linear Programs under Objective Uncertainty: A Completely Positive Representation (with Zheng Zhichao and Teo Chung-Piaw) Operations Research, 59, no. 3 (2011): 713-728 [PDF] [Additional Material]
  • Beyond Risk: Ambiguity in Supply Chains (with Melvyn Sim and Teo Chung-Piaw) Book Chapter Handbook of Integrated Risk Management in Global Supply Chains, edited by P .Kouvelis, O. Boyabatli, L. Dong, and R. Li, John Wiley & Sons Inc. (2011): 103-124


  • Tractable Robust Expected Utility and Risk Models for Portfolio Optimization (with Melvyn Sim and Joline Uichanco) Mathematical Finance, 20, no. 4 (2010): 695-731 [PDF]
  • Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion (with Dimitris Bertsimas, Xuan Vinh Doan and Chung-Piaw Teo) Mathematics of Operations Research, 35, no. 3 (2010): 580-602 [PDF]


  • Constructing Risk Measures from Uncertainty Sets (with Melvyn Sim and Dessislava Pachamanova) Operations Research, 57, no. 5 (2009): 1129-1141 [PDF] [Additional Material]
  • Persistency Model and Its Applications in Choice Modeling (with Song Miao and Teo Chung-Piaw) Management Science, 55, no. 3 (2009): 453-469 [PDF]


  • Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization (with Melvyn Sim and Dessislava Pachamanova) Management Science, 54, no. 3 (2008): pp. 573-585 [PDF]


  • A Semidefinite Approach to the Steady-State Analysis of Queueing Systems (with Dimitris Bertsimas) Queueing Systems, 56, no. 1 (2007): 27-39 [PDF]
  • A Mean-Variance Bound For A Three-Piece Linear Function (with Zhou Linyi) Probability in Engineering and Informational Sciences, 21, no. 4 (2007): 611-621 [PDF]
  • Use of Games and Projects in Teaching Applied Mathematics Courses. Experiments in Pedagogy: Selected Papers from Professional Development Programme (Teaching), Volume Two, Centre for Development of Teaching and Learning (2007)


  • Persistence in Discrete Optimization under Data Uncertainty (with Dimitris Bertsimas and Teo Chung-Piaw) Mathematical Programming Series B, Issue on Optimization under Uncertainty, 108, no. 2-3 (2006): 251-274 [PDF]
  • Tight Bounds on Expected Order Statistics (with Dimitris Bertsimas and Teo Chung-Piaw) Probability in Engineering and Informational Sciences, 20, no. 4 (2006): 667-686 [PDF]


  • Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming & Asymptotic Bounds (with Dimitris Bertsimas and Teo Chung-Piaw) SIAM Journal on Optimization, 15, no. 1 (2004): 185-209 [PDF]
  • Dispatching Automated Guided Vehicles in a Container Terminal (with Cheng Yong Leong, Sen Hock Chan, Teo Chung-Piaw and Tan Kok Choon) Supply Chain Optimization, J. Geunes, P.M. Pardalos eds., 98 (2005): pp. 355-390. Kluwer Academic Publishers [PDF]
  • Probabilistic Combinatorial Optimization: A Convex Programming Approach. PhD Thesis 2004. [Available on request]

General Talks

  • On the Interplay of Optimization and Probability in Decision-Making [PDF]