Robust linear optimization under general norms

Bertsimas, Dimitris; Pachamanova, Dessislava A.; Sim, Melvyn

doi:10.1016/j.orl.2003.12.007

Cited by 390 publications

(219 citation statements)

References 11 publications

(29 reference statements)

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“…11], [19][20][21]. These were followed by many results for specific problem classes or applications; see, e.g., the survey [22]; examples include robust linear programs [2,23,24], robust least-squares [25,26], robust quadratically constrained programs [27], robust semidefinite programs [28], robust conic programming [29], robust discrete optimization [30]. Work focused on specific applications includes robust control [31,32], robust portfolio optimization [33][34][35][36], robust beamforming [37][38][39], robust machine learning [40], and many others.…”

Section: Worst-case Robust Optimizationmentioning

confidence: 99%

Cutting-set methods for robust convex optimization with pessimizing oracles

Mutapcic

Boyd

2009

Optimization Methods and Software

128

170

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We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.

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Section: Worst-case Robust Optimizationmentioning

confidence: 99%

Cutting-set methods for robust convex optimization with pessimizing oracles

Mutapcic

Boyd

2009

Optimization Methods and Software

128

170

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“…Typically, the uncertainty set is convex. Its size is frequently related to some kind of guarantees on the probability that the constraint involving the uncertain data will not be violated (El Ghaoui et al [16,15], Ben-Tal and Nemirovski [4], Bertsimas and Sim [7], Bertsimas et al [8], Chen et al [12]). …”

Section: Robust Counterpart Risk Measuresmentioning

confidence: 99%

Constructing Risk Measures from Uncertainty Sets

Natarajan

Pachamanova

Sim

2009

Operations Research

Self Cite

150

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We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can in fact construct coherent risk measures. Our approach to creating coherent risk measures is easy to apply in practice, and computational experiments suggest that it may lead to superior portfolio performance. Our results have implications for efficient portfolio optimization under different measures of risk.

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“…The robust counterpart of the stochastic program is derived in view of the pre-specified uncertainty set. This is a deterministic model that does not involve an uncertain parameter, Bertsimas et al, (2004). Most importantly, the robust model becomes computationally tractable.…”

Section: Accepted Manuscriptmentioning

confidence: 99%