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199
LINEAR FRACTIONAL PROGRAM UNDER INTERVAL AND ELLIPSOIDAL UNCERTAINTY
"... In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional program ..."
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In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional
Linear Data Fitting Problems under Ellipsoidal Uncertainty
"... The purpose of this paper is to give a concise exposition of some recent developments in the formulation of robust counterpart programs in the sense of BenTal and Nemirovski [2] in the context of linear data fitting problems where the data elements are subject to ellipsoidal uncertainty. In additio ..."
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The purpose of this paper is to give a concise exposition of some recent developments in the formulation of robust counterpart programs in the sense of BenTal and Nemirovski [2] in the context of linear data fitting problems where the data elements are subject to ellipsoidal uncertainty
Robust discrete optimization under ellipsoidal uncertainty sets
, 2004
"... We address the complexity and practically e cient methods for robust discrete optimization under ellipsoidal uncertainty sets. Speci cally, weshowthat the robust counterpart of a discrete optimization problem with correlated objective function data is NPhard even though the nominal problem is polyn ..."
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Cited by 11 (0 self)
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We address the complexity and practically e cient methods for robust discrete optimization under ellipsoidal uncertainty sets. Speci cally, weshowthat the robust counterpart of a discrete optimization problem with correlated objective function data is NPhard even though the nominal problem
Towards a Combination of Interval and Ellipsoid Uncertainty
"... In many reallife situations, we do not know the probability distribution of measurement errors (∆x1,..., ∆xn), we only know the upper bounds ∆i on these errors. In such situations, once we know the measurement results ˜x1,..., ˜xn, we can only conclude that the actual (unknown) values of the quanti ..."
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algorithm for computing the range of a linear function f. In some cases, however, we have a combination of interval and ellipsoid uncertainty. In this case, the actual values (∆x1,..., ∆xn) belong to the intersection of the box x1 ×...×xn and the ellipsoid. In general, estimating the range over
LMIs for Robust Stabilization of Systems with Ellipsoidal Uncertainty
"... A recently developed ellipsoidal inner approximation of the stability domain in the space of polynomial coefficients is used to show that the problem of robust stabilization of a scalar plant affected by ellipsoidal parametric uncertainty boils down to a mere convex LMI problem. An illustrative n ..."
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A recently developed ellipsoidal inner approximation of the stability domain in the space of polynomial coefficients is used to show that the problem of robust stabilization of a scalar plant affected by ellipsoidal parametric uncertainty boils down to a mere convex LMI problem. An illustrative
Conditional ValueatRisk under ellipsoidal uncertainties
"... Although ValueatRisk (VaR) has been widely adapted in financial management, Conditional Valueatrisk (CVaR), which is also known as mean excess loss, mean shortfall, or tail VaR, has also gained importance over the past decade. This is largely owing to the more appealing mathematical properties o ..."
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of the latter. Based on Rockafellar and Uryasev’s idea, we are going to look into the CVaR under an ellipsoidal distribution. With the adhoc primaldual interiorpoint algorithm, we will also focus on the technique that minimizes the CVaR under the framework of portfolio selection.
Robust portfolio selection based on a joint ellipsoidal uncertainty set
"... . For these uncertainty sets, each type of uncertain parameter (e.g. mean and covariance) has its own uncertainty set. As addressed in [Z. Lu, A new cone programming approach for robust portfolio selection, Tech. Rep., Department of Mathematics, Simon Fraser University, Burnaby, BC, 2006; Z. Lu, A ..."
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computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set, Math. Program. (2009), DOI: 10.1007/5101070090271z], these 'separable' uncertainty sets typically share two common properties: (1) their actual confidence level, namely, the probability of uncertain
OPERA: OPtimization with Ellipsoidal uncertainty for Robust Analog IC design
"... As the designmanufacturing interface becomes increasingly complicated with IC technology scaling, the corresponding process variability poses great challenges for nanoscale analog/RF design. Design optimization based on the enumeration of process corners has been widely used, but can suffer from ..."
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specified confidence ellipsoid. Using such optimization with ellipsoidal uncertainty approach, robust design can be obtained with guaranteed yield bound and lower design cost, and most importantly, the problem size grows linearly with number of uncertain parameters. Numerical examples demonstrate the efficiency
Robust portfolio selection based on a joint ellipsoidal uncertainty set
 Optimization Methods & Software
, 2011
"... The “separable ” uncertainty sets have been widely used in robust portfolio selection models (e.g., see [16, 15, 28]). For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [21, 22], these “separable ” uncertainty sets ..."
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Cited by 2 (0 self)
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” ellipsoidal uncertainty set for the model parameters and show that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters. We further show that the robust maximum riskadjusted return (RMRAR) problem with this uncertainty set can
Doubly Constrained Robust Capon Beamformer with Ellipsoidal Uncertainty Sets 1
"... The doubly constrained robust (DCR) Capon beamformer with a spherical uncertainty set was introduced and studied in [1], [2]. Here we consider the generalized DCR problem (GDCR) in which the uncertainty set is an ellipsoid rather than a sphere. Although, as noted previously in [2], this problem is n ..."
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Cited by 14 (1 self)
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The doubly constrained robust (DCR) Capon beamformer with a spherical uncertainty set was introduced and studied in [1], [2]. Here we consider the generalized DCR problem (GDCR) in which the uncertainty set is an ellipsoid rather than a sphere. Although, as noted previously in [2], this problem
Results 1  10
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199