A survey of nonlinear robust optimization

Leyffer, Sven; Menickelly, Matt; Munson, Todd; Vanaret, Charlie; Wild, Stefan M.

doi:10.1080/03155986.2020.1730676

Title: A survey of nonlinear robust optimization

Journal Article · Tue Mar 17 00:00:00 EDT 2020 · INFOR. Information Systems and Operational Research

DOI:https://doi.org/10.1080/03155986.2020.1730676· OSTI ID:1660707

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Argonne National Lab. (ANL), Lemont, IL (United States)

Robust optimization (RO) has attracted great attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1660707

Journal Information:: INFOR. Information Systems and Operational Research, Vol. 58, Issue 2; ISSN 0315-5986

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 21 works

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References (98)

Hidden conic quadratic representation of some nonconvex quadratic optimization problems Ben-Tal, Aharon; den Hertog, Dick Mathematical Programming, Vol. 143, Issue 1-2 https://doi.org/10.1007/s10107-013-0710-8	journal	September 2013
A derivative-free approximate gradient sampling algorithm for finite minimax problems Hare, W.; Nutini, J. Computational Optimization and Applications, Vol. 56, Issue 1 https://doi.org/10.1007/s10589-013-9547-6	journal	March 2013
Robust optimization – A comprehensive survey Beyer, Hans-Georg; Sendhoff, Bernhard Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 33-34 https://doi.org/10.1016/j.cma.2007.03.003	journal	July 2007
A survey of adjustable robust optimization Yanıkoğlu, İhsan; Gorissen, Bram L.; den Hertog, Dick European Journal of Operational Research, Vol. 277, Issue 3 https://doi.org/10.1016/j.ejor.2018.08.031	journal	September 2019
Distributionally Robust Convex Optimization Wiesemann, Wolfram; Kuhn, Daniel; Sim, Melvyn Operations Research, Vol. 62, Issue 6 https://doi.org/10.1287/opre.2014.1314	journal	December 2014
Robust support vector machines for classification and computational issues Trafalis, T. B.; Gilbert, R. C. Optimization Methods and Software, Vol. 22, Issue 1 https://doi.org/10.1080/10556780600883791	journal	February 2007
Safe Approximations of Ambiguous Chance Constraints Using Historical Data Yanıkoğlu, İhsan; den Hertog, Dick INFORMS Journal on Computing, Vol. 25, Issue 4 https://doi.org/10.1287/ijoc.1120.0529	journal	November 2013
Cutting plane versus compact formulations for uncertain (integer) linear programs Fischetti, Matteo; Monaci, Michele Mathematical Programming Computation, Vol. 4, Issue 3 https://doi.org/10.1007/s12532-012-0039-y	journal	April 2012
Bilevel derivative-free optimization and its application to robust optimization Conn, A. R.; Vicente, L. N. Optimization Methods and Software, Vol. 27, Issue 3 https://doi.org/10.1080/10556788.2010.547579	journal	June 2012
An approximation technique for robust nonlinear optimization Diehl, Moritz; Bock, Hans Georg; Kostina, Ekaterina Mathematical Programming, Vol. 107, Issue 1-2 https://doi.org/10.1007/s10107-005-0685-1	journal	December 2005
ROPI—a robust optimization programming interface for C++ Goerigk, Marc Optimization Methods and Software, Vol. 29, Issue 6 https://doi.org/10.1080/10556788.2013.869807	journal	February 2014
Data-driven chance constrained stochastic program Jiang, Ruiwei; Guan, Yongpei Mathematical Programming, Vol. 158, Issue 1-2 https://doi.org/10.1007/s10107-015-0929-7	journal	July 2015
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations Mohajerin Esfahani, Peyman; Kuhn, Daniel Mathematical Programming, Vol. 171, Issue 1-2 https://doi.org/10.1007/s10107-017-1172-1	journal	July 2017
Interior-Point Algorithms, Penalty Methods and Equilibrium Problems Benson, Hande Y.; Sen, Arun; Shanno, David F. Computational Optimization and Applications, Vol. 34, Issue 2 https://doi.org/10.1007/s10589-005-3908-8	journal	March 2006
Modeling and solving uncertain optimization problems in YALMIP Löfberg, Johan IFAC Proceedings Volumes, Vol. 41, Issue 2 https://doi.org/10.3182/20080706-5-KR-1001.00229	journal	January 2008
Global Convergence of an Elastic Mode Approach for a Class of Mathematical Programs with Complementarity Constraints Anitescu, Mihai SIAM Journal on Optimization, Vol. 16, Issue 1 https://doi.org/10.1137/040606855	journal	January 2005
Theory and Applications of Robust Optimization Bertsimas, Dimitris; Brown, David B.; Caramanis, Constantine SIAM Review, Vol. 53, Issue 3 https://doi.org/10.1137/080734510	journal	January 2011
Nonlinear MPC of kites under varying wind conditions for a new class of large-scale wind power generators Ilzhöfer, A.; Houska, B.; Diehl, M. International Journal of Robust and Nonlinear Control, Vol. 17, Issue 17 https://doi.org/10.1002/rnc.1210	journal	January 2007
Robust Control of Markov Decision Processes with Uncertain Transition Matrices Nilim, Arnab; El Ghaoui, Laurent Operations Research, Vol. 53, Issue 5 https://doi.org/10.1287/opre.1050.0216	journal	October 2005
Robust Truss Topology Design via Semidefinite Programming Ben-Tal, A.; Nemirovski, A. SIAM Journal on Optimization, Vol. 7, Issue 4 https://doi.org/10.1137/S1052623495291951	journal	November 1997
Robust convex quadratically constrained programs Goldfarb, D.; Iyengar, G. Mathematical Programming, Vol. 97, Issue 3 https://doi.org/10.1007/s10107-003-0425-3	journal	August 2003
The adaptive convexification algorithm for semi-infinite programming with arbitrary index sets Stein, Oliver; Steuermann, Paul Mathematical Programming, Vol. 136, Issue 1 https://doi.org/10.1007/s10107-012-0556-5	journal	May 2012
A successive SDP-NSDP approach to a robust optimization problem in finance Leibfritz, F.; Maruhn, J. H. Computational Optimization and Applications, Vol. 44, Issue 3 https://doi.org/10.1007/s10589-007-9163-4	journal	January 2008
A Robust Optimization Approach for Magnetic Spacecraft Attitude Stabilization Bruni, Renato; Celani, Fabio Journal of Optimization Theory and Applications, Vol. 173, Issue 3 https://doi.org/10.1007/s10957-016-1035-6	journal	November 2016
A practical guide to robust optimization Gorissen, Bram L.; Yanıkoğlu, İhsan; den Hertog, Dick Omega, Vol. 53 https://doi.org/10.1016/j.omega.2014.12.006	journal	June 2015
Uncertainty analysis and robust optimization of multiscale process systems with application to epitaxial thin film growth Rasoulian, Shabnam; Ricardez-Sandoval, Luis Alberto Chemical Engineering Science, Vol. 116 https://doi.org/10.1016/j.ces.2014.05.027	journal	September 2014
Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations Lass, Oliver; Ulbrich, Stefan SIAM Journal on Scientific Computing, Vol. 39, Issue 5 https://doi.org/10.1137/16M108269X	journal	January 2017
Expected improvement based infill sampling for global robust optimization of constrained problems ur Rehman, Samee; Langelaar, Matthijs Optimization and Engineering, Vol. 18, Issue 3 https://doi.org/10.1007/s11081-016-9346-x	journal	January 2017
Interior Methods for Mathematical Programs with Complementarity Constraints Leyffer, Sven; López-Calva, Gabriel; Nocedal, Jorge SIAM Journal on Optimization, Vol. 17, Issue 1 https://doi.org/10.1137/040621065	journal	January 2006
Robust Convex Optimization Ben-Tal, A.; Nemirovski, A. Mathematics of Operations Research, Vol. 23, Issue 4 https://doi.org/10.1287/moor.23.4.769	journal	November 1998
Robust optimization ? methodology and applications Ben-Tal, Aharon; Nemirovski, Arkadi Mathematical Programming, Vol. 92, Issue 3 https://doi.org/10.1007/s101070100286	journal	May 2002
Process scheduling under uncertainty: Review and challenges Li, Zukui; Ierapetritou, Marianthi Computers & Chemical Engineering, Vol. 32, Issue 4-5 https://doi.org/10.1016/j.compchemeng.2007.03.001	journal	April 2008
A log-robust optimization approach to portfolio management Kawas, Ban; Thiele, Aurélie OR Spectrum, Vol. 33, Issue 1 https://doi.org/10.1007/s00291-008-0162-3	journal	January 2009
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs Scherer, C. W.; Hol, C. W. J. Mathematical Programming, Vol. 107, Issue 1-2 https://doi.org/10.1007/s10107-005-0684-2	journal	December 2005
Robust Dynamic Optimization of a Semi-Batch Emulsion Polymerization Process with Parametric Uncertainties-A Heuristic Approach - Puschke, Jennifer; Mitsos, Alexander IFAC-PapersOnLine, Vol. 49, Issue 7 https://doi.org/10.1016/j.ifacol.2016.07.305	journal	January 2016
A Distributional Interpretation of Robust Optimization Xu, Huan; Caramanis, Constantine; Mannor, Shie Mathematics of Operations Research, Vol. 37, Issue 1 https://doi.org/10.1287/moor.1110.0531	journal	February 2012
A two-sided relaxation scheme for Mathematical Programs with Equilibrium Constraints DeMiguel, Victor; Friedlander, Michael P.; Nogales, Francisco J. SIAM Journal on Optimization, Vol. 16, Issue 2 https://doi.org/10.1137/04060754x	journal	January 2005
Optimization of conditional value-at-risk Rockafellar, R. Tyrrell; Uryasev, Stanislav The Journal of Risk, Vol. 2, Issue 3 https://doi.org/10.21314/JOR.2000.038	journal	January 2000
Short sales in Log-robust portfolio management Kawas, Ban; Thiele, Aurélie European Journal of Operational Research, Vol. 215, Issue 3 https://doi.org/10.1016/j.ejor.2011.06.042	journal	December 2011
Solving mathematical programs with complementarity constraints as nonlinear programs Fletcher*, Roger; Leyffer,‡, Sven Optimization Methods and Software, Vol. 19, Issue 1 https://doi.org/10.1080/10556780410001654241	journal	February 2004
Recent advances in robust optimization: An overview Gabrel, Virginie; Murat, Cécile; Thiele, Aurélie European Journal of Operational Research, Vol. 235, Issue 3 https://doi.org/10.1016/j.ejor.2013.09.036	journal	June 2014
Robust Solutions of Optimization Problems Affected by Uncertain Probabilities Ben-Tal, Aharon; den Hertog, Dick; De Waegenaere, Anja Management Science, Vol. 59, Issue 2 https://doi.org/10.1287/mnsc.1120.1641	journal	February 2013
A Second Order Approximation Technique for Robust Shape Optimization Sichau, Adrian; Ulbrich, Stefan Applied Mechanics and Materials, Vol. 104 https://doi.org/10.4028/www.scientific.net/AMM.104.13	journal	September 2011
Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model Rusmevichientong, Paat; Topaloglu, Huseyin Operations Research, Vol. 60, Issue 4 https://doi.org/10.1287/opre.1120.1063	journal	August 2012
Robust airfoil optimization to achieve drag reduction over a range of Mach numbers Li, W.; Huyse, L.; Padula, S. Structural and Multidisciplinary Optimization, Vol. 24, Issue 1 https://doi.org/10.1007/s00158-002-0212-4	journal	August 2002
An Interior Point Method for Mathematical Programs with Complementarity Constraints (MPCCs) Raghunathan, Arvind U.; Biegler, Lorenz T. SIAM Journal on Optimization, Vol. 15, Issue 3 https://doi.org/10.1137/S1052623403429081	journal	January 2005
Robust Optimization Made Easy with ROME Goh, Joel; Sim, Melvyn Operations Research, Vol. 59, Issue 4 https://doi.org/10.1287/opre.1110.0944	journal	August 2011
Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures Postek, Krzysztof; den Hertog, Dick; Melenberg, Bertrand SIAM Review, Vol. 58, Issue 4 https://doi.org/10.1137/151005221	journal	January 2016
Solving Semi-Infinite Optimization Problems with Interior Point Techniques Stein, Oliver; Still, Georg SIAM Journal on Control and Optimization, Vol. 42, Issue 3 https://doi.org/10.1137/S0363012901398393	journal	January 2003
Some outer approximation methods for semi-infinite optimization problems Reemtsen, Rembert Journal of Computational and Applied Mathematics, Vol. 53, Issue 1 https://doi.org/10.1016/0377-0427(92)00122-P	journal	July 1994
Robust Optimization Ben-Tal, Aharon; El Ghaoui, Laurent; Nemirovski, Arkadi Princeton Series in Applied Mathematics https://doi.org/10.1515/9781400831050	book	December 2009
An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty Kolvenbach, Philip; Lass, Oliver; Ulbrich, Stefan Optimization and Engineering, Vol. 19, Issue 3 https://doi.org/10.1007/s11081-018-9388-3	journal	June 2018
Likelihood robust optimization for data-driven problems Wang, Zizhuo; Glynn, Peter W.; Ye, Yinyu Computational Management Science, Vol. 13, Issue 2 https://doi.org/10.1007/s10287-015-0240-3	journal	September 2015
Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach Ghaoui, Laurent El; Oks, Maksim; Oustry, Francois Operations Research, Vol. 51, Issue 4 https://doi.org/10.1287/opre.51.4.543.16101	journal	August 2003
Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems Delage, Erick; Ye, Yinyu Operations Research, Vol. 58, Issue 3 https://doi.org/10.1287/opre.1090.0741	journal	June 2010
Convex Approximations of Chance Constrained Programs Nemirovski, Arkadi; Shapiro, Alexander SIAM Journal on Optimization, Vol. 17, Issue 4 https://doi.org/10.1137/050622328	journal	January 2007
Robust Portfolio Selection Problems Goldfarb, D.; Iyengar, G. Mathematics of Operations Research, Vol. 28, Issue 1 https://doi.org/10.1287/moor.28.1.1.14260	journal	February 2003
Chance constrained uncertain classification via robust optimization Ben-Tal, Aharon; Bhadra, Sahely; Bhattacharyya, Chiranjib Mathematical Programming, Vol. 127, Issue 1 https://doi.org/10.1007/s10107-010-0415-1	journal	October 2010
Deriving robust counterparts of nonlinear uncertain inequalities Ben-Tal, Aharon; den Hertog, Dick; Vial, Jean-Philippe Mathematical Programming, Vol. 149, Issue 1-2 https://doi.org/10.1007/s10107-014-0750-8	journal	February 2014
Robust portfolio optimization with derivative insurance guarantees Zymler, Steve; Rustem, Berç; Kuhn, Daniel European Journal of Operational Research, Vol. 210, Issue 2 https://doi.org/10.1016/j.ejor.2010.09.027	journal	April 2011
A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints Liu, Xinwei; Perakis, Georgia; Sun, Jie Computational Optimization and Applications, Vol. 34, Issue 1 https://doi.org/10.1007/s10589-005-3075-y	journal	October 2005
Robust solutions of uncertain linear programs Ben-Tal, A.; Nemirovski, A. Operations Research Letters, Vol. 25, Issue 1 https://doi.org/10.1016/S0167-6377(99)00016-4	journal	August 1999
SIPAMPL: Semi-infinite programming with AMPL Vaz, A. Ismael F.; Fernandes, Edite M. G. P.; Gomes, M. Paula S. F. ACM Transactions on Mathematical Software, Vol. 30, Issue 1 https://doi.org/10.1145/974781.974784	journal	March 2004
Duality in robust optimization: Primal worst equals dual best Beck, Amir; Ben-Tal, Aharon Operations Research Letters, Vol. 37, Issue 1 https://doi.org/10.1016/j.orl.2008.09.010	journal	January 2009
Data-driven robust optimization Bertsimas, Dimitris; Gupta, Vishal; Kallus, Nathan Mathematical Programming, Vol. 167, Issue 2 https://doi.org/10.1007/s10107-017-1125-8	journal	February 2017
An Outer Approximations Approach to Reliability-Based Optimal Design of Structures Kirjner-Neto, C.; Polak, E.; Kiureghian, A. Der Journal of Optimization Theory and Applications, Vol. 98, Issue 1 https://doi.org/10.1023/A:1022647728419	journal	July 1998
Optimization under Decision-Dependent Uncertainty Nohadani, Omid; Sharma, Kartikey SIAM Journal on Optimization, Vol. 28, Issue 2 https://doi.org/10.1137/17M1110560	journal	January 2018
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints Fletcher, Roger; Leyffer, Sven; Ralph, Danny SIAM Journal on Optimization, Vol. 17, Issue 1 https://doi.org/10.1137/S1052623402407382	journal	January 2006
Derivative-Free Robust Optimization for Circuit Design Ciccazzo, Angelo; Latorre, Vittorio; Liuzzi, Giampaolo Journal of Optimization Theory and Applications, Vol. 164, Issue 3 https://doi.org/10.1007/s10957-013-0441-2	journal	October 2013
Robust Solutions to Uncertain Semidefinite Programs El Ghaoui, Laurent; Oustry, Francois; Lebret, Hervé SIAM Journal on Optimization, Vol. 9, Issue 1 https://doi.org/10.1137/S1052623496305717	journal	January 1998
Robust Regression and Lasso Xu, Huan; Caramanis, Constantine; Mannor, Shie IEEE Transactions on Information Theory, Vol. 56, Issue 7 https://doi.org/10.1109/TIT.2010.2048503	journal	July 2010
Robust PCA via Outlier Pursuit Xu, Huan; Caramanis, Constantine; Sanghavi, Sujay IEEE Transactions on Information Theory, Vol. 58, Issue 5 https://doi.org/10.1109/TIT.2011.2173156	journal	May 2012
Robust portfolio optimization: a conic programming approach Ye, Kai; Parpas, Panos; Rustem, Berç Computational Optimization and Applications, Vol. 52, Issue 2 https://doi.org/10.1007/s10589-011-9419-x	journal	June 2011
A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance Kim, Seung-Jean; Boyd, Stephen SIAM Journal on Optimization, Vol. 19, Issue 3 https://doi.org/10.1137/060677586	journal	January 2008
YALMIP : a toolbox for modeling and optimization in MATLAB Lofberg, J. 2004 IEEE International Symposium on Computer Aided Control Systems Design, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) https://doi.org/10.1109/CACSD.2004.1393890	conference	January 2004
Symmetry groups, semidefinite programs, and sums of squares Gatermann, Karin; Parrilo, Pablo A. Journal of Pure and Applied Algebra, Vol. 192, Issue 1-3 https://doi.org/10.1016/j.jpaa.2003.12.011	journal	September 2004
Derivative-free optimization methods for finite minimax problems Hare, Warren; Macklem, Mason Optimization Methods and Software, Vol. 28, Issue 2 https://doi.org/10.1080/10556788.2011.638923	journal	April 2013
Semi-Infinite Programming: Theory, Methods, and Applications Hettich, R.; Kortanek, K. O. SIAM Review, Vol. 35, Issue 3 https://doi.org/10.1137/1035089	journal	September 1993
Worst-Case Value at Risk of Nonlinear Portfolios Zymler, Steve; Kuhn, Daniel; Rustem, Berç Management Science, Vol. 59, Issue 1 https://doi.org/10.1287/mnsc.1120.1615	journal	January 2013
Case Studies for a First-Order Robust Nonlinear Programming Formulation Hale, E. T.; Zhang, Y. Journal of Optimization Theory and Applications, Vol. 134, Issue 1 https://doi.org/10.1007/s10957-007-9208-y	journal	May 2007
Robust Optimization for Unconstrained Simulation-Based Problems Bertsimas, Dimitris; Nohadani, Omid; Teo, Kwong Meng Operations Research, Vol. 58, Issue 1 https://doi.org/10.1287/opre.1090.0715	journal	February 2010
Portfolio Selection with Robust Estimation DeMiguel, Victor; Nogales, Francisco J. Operations Research, Vol. 57, Issue 3 https://doi.org/10.1287/opre.1080.0566	journal	June 2009
Distributionally robust joint chance constraints with second-order moment information Zymler, Steve; Kuhn, Daniel; Rustem, Berç Mathematical Programming, Vol. 137, Issue 1-2 https://doi.org/10.1007/s10107-011-0494-7	journal	November 2011
Robust solutions of Linear Programming problems contaminated with uncertain data Ben-Tal, Aharon; Nemirovski, Arkadi Mathematical Programming, Vol. 88, Issue 3 https://doi.org/10.1007/PL00011380	journal	September 2000
Algorithmic differentiation for piecewise smooth functions: a case study for robust optimization Fiege, Sabrina; Walther, Andrea; Kulshreshtha, Kshitij Optimization Methods and Software, Vol. 33, Issue 4-6 https://doi.org/10.1080/10556788.2017.1333613	journal	June 2017
Robust optimization in electromagnetic scattering problems Bertsimas, Dimitris; Nohadani, Omid; Teo, Kwong Meng Journal of Applied Physics, Vol. 101, Issue 7 https://doi.org/10.1063/1.2715540	journal	April 2007
Distributionally Robust Optimization and Its Tractable Approximations Goh, Joel; Sim, Melvyn Operations Research, Vol. 58, Issue 4-part-1 https://doi.org/10.1287/opre.1090.0795	journal	August 2010
Robust Optimization with Ambiguous Stochastic Constraints Under Mean and Dispersion Information Postek, Krzysztof; Ben-Tal, Aharon; den Hertog, Dick Operations Research, Vol. 66, Issue 3 https://doi.org/10.1287/opre.2017.1688	journal	June 2018
Numerical solution approaches for robust nonlinear optimal control problems Diehl, Moritz; Gerhard, Johannes; Marquardt, Wolfgang Computers & Chemical Engineering, Vol. 32, Issue 6 https://doi.org/10.1016/j.compchemeng.2007.06.002	journal	June 2008
Adaptive Distributionally Robust Optimization Bertsimas, Dimitris; Sim, Melvyn; Zhang, Meilin Management Science, Vol. 65, Issue 2 https://doi.org/10.1287/mnsc.2017.2952	journal	February 2019
Nonlinear robust optimization for process design Yuan, Yuan; Li, Zukui; Huang, Biao AIChE Journal, Vol. 64, Issue 2 https://doi.org/10.1002/aic.15950	journal	September 2017
Distributionally Robust Stochastic Programming Shapiro, Alexander SIAM Journal on Optimization, Vol. 27, Issue 4 https://doi.org/10.1137/16M1058297	journal	January 2017
Reformulation versus cutting-planes for robust optimization: A computational study Bertsimas, Dimitris; Dunning, Iain; Lubin, Miles Computational Management Science, Vol. 13, Issue 2 https://doi.org/10.1007/s10287-015-0236-z	journal	July 2015
On Distributionally Robust Chance-Constrained Linear Programs Calafiore, G. C.; Ghaoui, L. El Journal of Optimization Theory and Applications, Vol. 130, Issue 1 https://doi.org/10.1007/s10957-006-9084-x	journal	December 2006
Distributionally robust chance constraints for non-linear uncertainties Yang, Wenzhuo; Xu, Huan Mathematical Programming, Vol. 155, Issue 1-2 https://doi.org/10.1007/s10107-014-0842-5	journal	November 2014
Robust optimization with simulated annealing Bertsimas, Dimitris; Nohadani, Omid Journal of Global Optimization, Vol. 48, Issue 2 https://doi.org/10.1007/s10898-009-9496-x	journal	December 2009
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION: tractable robust expected utility and risk models Natarajan, Karthik; Sim, Melvyn; Uichanco, Joline Mathematical Finance, Vol. 20, Issue 4 https://doi.org/10.1111/j.1467-9965.2010.00417.x	journal	September 2010
Robust Optimization of Large-Scale Systems Mulvey, John M.; Vanderbei, Robert J.; Zenios, Stavros A. Operations Research, Vol. 43, Issue 2 https://doi.org/10.1287/opre.43.2.264	journal	April 1995

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