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In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO).
The use of multiple measurements in taxonomic problems
R.A. Fisher · 1936
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Portfolio selection
H.M. Markowitz · 1952
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Theory of capacities
G. Choquet · 1954
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Linear programming under uncertainty
G.B. Dantzig · 1955
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Portfolio Selection
H.M. Markowitz · 1959
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On the field of values of a matrix
L. Brickman · 1961
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Convex programming with set-inclusive constraints and applications to inexact linear programming
A.L. Soyster · 1973
Earlier work this paper cites.
Computers and Intractability: A Guide to the Theory of NP-Completeness
M. Garey and D. Johnson · 1979
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Robust Statistics
P. Huber · 1981
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Postoptimal analysis of a linear program under simultaneous changes in matrix coefficients
R. Freund · 1985
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Integral representation without additivity
D. Schmeidler · 1986
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Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics
M.K.H. Fan, A. Tits, and J. Doyle · 1991
Earlier work this paper cites.
Several NP-hard problems arising in robust stability analysis
A. Nemirovski · 1993
Earlier work this paper cites.
Linear Matrix Inequalities in System and Control Theory
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan · 1994
Earlier work this paper cites.
Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs
G. Infanger · 1994
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Stochastic Programming
P. Kall and S. Wallace · 1994
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Markov Decision Processes: Discrete Stochastic Dynamic Programming
M. Puterman · 1994
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Some perturbation theory for linear programming
J. Renegar · 1994
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H ∞ H^{\infty} -Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach
T. Başar and P. Bernhard · 1995
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Dynamic Programming and Optimal Control
D.P. Bertsekas · 1995
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Optimization over state feedback policies for robust control with constraints
P.J. Goulart, E.C. Kerrigan, and J.M. Maciejowski · 1995
Earlier work this paper cites.
Stochastic Programming
A. Prékopa · 1995
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Neuro Dynamic Programming
D. Bertsekas and J.N. Tsitsiklis · 1996
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Semidefinite programming
S. Boyd and L. Vandenberghe · 1996
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Robust and Optimal Control
K. Zhou, J.C. Doyle, and K. Glover · 1996
Earlier work this paper cites.
Robust truss topology design via semindefinite programming
A. Ben-Tal and A. Nemirovski · 1997
Earlier work this paper cites.
Introduction to Linear Optimization
D. Bertsimas and J. Tsitsiklis · 1997
Earlier work this paper cites.
Introduction to Stochastic Programming
J.R. Birge and F. Louveaux · 1997
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Robust solutions to least-squares problems with uncertain data
L. El Ghaoui and H. Lebret · 1997
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Robust discrete optimization and its applications
P. Kouvelis and G. Yu · 1997
Earlier work this paper cites.
Robust convex optimization
A. Ben-Tal and A. Nemirovski · 1998
Earlier work this paper cites.
Robust solutions to uncertain semidefinite programs
L. El Ghaoui, F. Oustry, and H. Lebret · 1998
Earlier work this paper cites.
Coherent measures of risk
P. Artzner, F. Delbaen, J. Eber, and D. Heath · 1999
Earlier work this paper cites.
Robust solutions of uncertain linear programs
A. Ben-Tal and A. Nemirovski · 1999
Earlier work this paper cites.
Atomic decomposition by basis pursuit
S. S. Chen, D. L. Donoho, and M. A. Saunders · 1999
Earlier work this paper cites.
A Course in Robust Control Theory: A Convex Approach
G.E. Dullerud and F. Paganini · 1999
Earlier work this paper cites.
Robust semidefinite programming
A. Ben-Tal, L. El Ghaoui, and A. Nemirovski · 2000
Earlier work this paper cites.
Robust modeling of multi-stage portfolio problems
A. Ben-Tal, T. Margalit, and A. Nemirovski · 2000
Earlier work this paper cites.
Robust solutions of linear programming problems contaminated with uncertain data
A. Ben-Tal and A. Nemirovski · 2000
Earlier work this paper cites.
Advances in linear matrix inequality methods in control: advances in design and control
L. El Ghaoui and S. Niculescu, editors · 2000
Earlier work this paper cites.
The worst-case risk of a portfolio
M.S. Lobo and S. Boyd · 2000
Earlier work this paper cites.
On approximate robust counterparts of uncertain semidefinite and conic quadratic programs
A. Ben-Tal and A. Nemirovski · 2001
Earlier work this paper cites.
Worst-case maximum likelihood estimation in the linear model
G. Calafiore and L. El Ghaoui · 2001
Earlier work this paper cites.
Stochastic algorithms for exact and approximate feasibility of robust lmis
G. Calafiore and B. Polyak · 2001
Earlier work this paper cites.
Robust control and model uncertainty
L. Hansen and T. Sargent · 2001
Cited alongside, same era.
On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty
A. Ben-Tal and A. Nemirovski · 2002
Cited alongside, same era.
Robust solutions of uncertain quadratic and conic-quadratic problems
A. Ben-Tal, A. Nemirovski, and C. Roos · 2002
Cited alongside, same era.
Robust portfolio selection using linear-matrix inequalities
O. Costa and A. Paiva · 2002
Cited alongside, same era.
Convex measures of risk and trading constraints
H. Föllmer and A. Schied · 2002
Cited alongside, same era.
A robust minimax approach to classification
G.R.G. Lanckriet, L. El Ghaoui, C. Bhattacharyya, and M.I. Jordan · 2002
Cited alongside, same era.
The scenario approach to robust control design
G. Calafiore and M. C. Campi · 2006
Later among the works it cites.
PhD dissertation, Massachusetts Institute of Technology, 2006
C. Caramanis · 2006
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Ambiguous chance constrained problems and robust optimization
E. Erdoğan and G. Iyengar · 2006
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Stochastic covering and adaptivity
M.X. Goemans and J. Vondrák · 2006
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An introduction to convex optimization for communications and signal processing
Z.Q. Luo and W. Yu · 2006
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Ambiguity aversion, robustness, and the variational representation of preferences
F. Maccheroni, M. Marinacci, and A. Rustichini · 2006
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Robust regularization
A.S. Lewis · 2002
Cited alongside, same era.
Adjustable robust solutions of uncertain linear programs
A. Ben-Tal, A. Goryashko, E. Guslitzer, and A. Nemirovski · 2003
Cited alongside, same era.
Robust discrete optimization and network flows
D. Bertsimas and M. Sim · 2003
Cited alongside, same era.
Worst-case value-at-risk and robust portfolio optimization: A conic programming approach
L. El Ghaoui, M. Oks, and F. Oustry · 2003
Cited alongside, same era.
Robust portfolio selection problems
D. Goldfarb and G. Iyengar · 2003
Cited alongside, same era.
Robust receding horizon control - analysis and synthesis
P. Grieder, P.A. Parrilo, and M. Morari · 2003
Cited alongside, same era.
Convex approximations of chance constrained programs
A. Nemirovski and A. Shapiro · 2006
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On complexity of multistage stochastic programs
A. Shapiro · 2006
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Second order cone programming approaches for handling missing and uncertain data
P. Shivaswamy, C. Bhattacharyya, and A.J. Smola · 2006
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Tradeoff performance and robustness in linear programming and markov decision processes
H. Xu and S. Mannor · 2006
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Two-stage robust network flow and design under demand uncertainty
A. Atamtürk and M. Zhang · 2007
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A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem
S. Benati and R. Rizzi · 2007
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Constrained Stochastic LQC: A Tractable Approach
D. Bertsimas and D.B. Brown · 2007
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Adaptability via sampling
D. Bertsimas and C. Caramanis · 2007
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Robust optimization in electromagnetic scattering problems
D. Bertsimas, O. Nohadani, and K.M. Teo · 2007
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A robust optimization perspective to stochastic programming
X. Chen, M. Sim, and P. Sun · 2007
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Power efficient buffer design using finite adaptable optimization
M. Mani, C. Caramanis, and M. Orshansky · 2007
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Beamforming with uncertain weights
A. Mutapcic, S.-J. Kim, and S. Boyd · 2007
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A survey of the s-lemma
I. Pólik and T. Terlaky · 2007
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Robust mean-covariance solutions for stochastic optimization
I. Popescu · 2007
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Optimal solutions for sparse principal component analysis
F. Bach A. d’Aspremont and L. El Ghaoui · 2008
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Computing robust basestock levels
D. Bienstock and N. Özbay · 2008
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Learning in the limit with adversarial disturbances
C. Caramanis and S. Mannor · 2008
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A linear-decision based approximation approach to stochastic programming
X. Chen, M. Sim, P. Sun, and J. Zhang · 2008
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Percentile optimization for markov decision processes with parameter uncertainty
E. Delage and S. Mannor · 2008
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Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data
O.Banerjee, L. El Ghaoui, and A. d’Aspremont · 2008
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System level optimization in wireless networks with uncertain customer arrival rates
S. Yun and C. Caramanis · 2008
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A soft robust model for optimization under ambiguity
A. Ben-Tal, D. Bertsimas, and D.B. Brown · 2009
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Robust Optimization
L. El Ghaoui Ben-Tal, A. and A. Nemirovski · 2009
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Constructing uncertainty sets for robust linear optimization
D. Bertsimas and D.B. Brown · 2009
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On the power of robust solutions in two-stage stochastic and adaptive optimization problems
D. Bertsimas and V. Goyal · 2009
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A hierarchy of suboptimal policies for the multi-period, multi-echelon, robust inventory problem
D. Bertsimas, D. Iancu, and P. Parrilo · 2009
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Optimality of affine policies in multi-stage robust optimization
D. Bertsimas, D. Iancu, and P. Parrilo · 2009
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Robust principal component analysis?
E.J. Candes, X. Li, Y. Ma, and J. Wright · 2009
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Distributionally robust optimization under moment uncertainty with application to data-driven problems
E. Delage and Y. Ye · 2009
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Constructing risk measures from uncertainty sets
K. Natarajan, D. Pachamanova, and M. Sim · 2009
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Exploiting sparsity in the matrix-dilation approach to robust semidefinite programming
Y. Oishi and Y. Isaka · 2009
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Mitigation of intra-array sram variability using adaptive voltage architecture
A. Singh, K. He, C. Caramanis, and M. Orshansky · 2009
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Robustness and regularization of support vector machines
H. Xu, C. Caramanis, and S. Mannor · 2009
Later among the works it cites.
Finite adaptability in linear optimization
D. Bertsimas and C. Caramanis · 2010
Closest in time.
A distributional interpretation of robust optimization
H. Xu, C. Caramanis, and S. Mannor · 2010
Closest in time.
Robust regression and Lasso
H. Xu, C. Caramanis, and S. Mannor · 2010
Closest in time.
Robust Optimization in Machine Learning
C. Caramanis, S. Mannor, and H. Xu · 2011
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