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Lectures on robust convex optimization
, 2012
"... Subject. The data of optimization problems of real world origin typically is uncertain not known exactly when the problem is solved. With the traditional approach, “small ” (fractions of percents) data uncertainty is merely ignored, and the problem is solved as if the nominal data — our guesses for ..."
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programs from the NETLIB library, 0.01 % random perturbations of uncertain data lead to more than 50 % violations of some of the constraints as evaluated at the nominal optimal solutions. Thus, in applications there is an actual need in a methodology which produces robust, “immunized against uncertainty
Convex Approximations of Chance Constrained Programs
"... We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given (close to one) probability, a system of randomly perturbed convex constraints. Our goal is to build a computationally tractable approximation of this (typically intractabl ..."
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Cited by 127 (6 self)
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intractable) problem, i.e., an explicitly given convex optimization program with the feasible set contained in the one of the chance constrained problem. We construct a general class of such convex conservative approximations of the corresponding chance constrained problem. Moreover, under the assumptions
Robust principal component analysis: Exact recovery of corrupted lowrank matrices via convex optimization
 Advances in Neural Information Processing Systems 22
, 2009
"... The supplementary material to the NIPS version of this paper [4] contains a critical error, which was discovered several days before the conference. Unfortunately, it was too late to withdraw the paper from the proceedings. Fortunately, since that time, a correct analysis of the proposed convex prog ..."
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Cited by 149 (4 self)
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programming relaxation has been developed by Emmanuel Candes of Stanford University. That analysis is reported in a joint paper, Robust Principal Component Analysis? by Emmanuel Candes, Xiaodong Li, Yi Ma and John Wright,
A maximum likelihood stereo algorithm
 Computer Vision and Image Understanding
, 1996
"... A stereo algorithm is presented that optimizes a maximum likelihood cost function. The maximum likelihood cost function assumes that corresponding features in the left and right images are Normally distributed about a common true value and consists of a weighted squared error term if two features ar ..."
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Cited by 234 (2 self)
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A stereo algorithm is presented that optimizes a maximum likelihood cost function. The maximum likelihood cost function assumes that corresponding features in the left and right images are Normally distributed about a common true value and consists of a weighted squared error term if two features
Automatic robust convex programming
, 2010
"... This paper presents the robust optimization framework in the modeling language YALMIP, which carries out robust modeling and uncertainty elimination automatically, and allows the user to concentrate on the highlevel model. While introducing the software package, a brief summary of robust optimizati ..."
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Cited by 2 (0 self)
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This paper presents the robust optimization framework in the modeling language YALMIP, which carries out robust modeling and uncertainty elimination automatically, and allows the user to concentrate on the highlevel model. While introducing the software package, a brief summary of robust
Uncertain convex programs: Randomized solutions and confidence levels
 MATH. PROGRAM., SER. A (2004)
, 2004
"... Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or ‘instance’ parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and ..."
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Cited by 115 (14 self)
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Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or ‘instance’ parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization
RASL: Robust Alignment by Sparse and Lowrank Decomposition for Linearly Correlated Images
, 2010
"... This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of ..."
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Cited by 161 (6 self)
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of errors and a lowrank matrix of recovered aligned images. We reduce this extremely challenging optimization problem to a sequence of convex programs that minimize the sum of ℓ1norm and nuclear norm of the two component matrices, which can be efficiently solved by scalable convex optimization techniques
Robust Optimization  Methodology and Applications
"... Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and se ..."
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Cited by 134 (6 self)
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and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained, or good approximations of these counterparts are proposed, making RO a useful tool for realworld applications. We discuss some of these applications, specifically: antenna
On the NesterovTodd direction in semidefinite programming
 SIAM JOURNAL ON OPTIMIZATION
, 1996
"... Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how ..."
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Cited by 132 (21 self)
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Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how
Highly Robust Error Correction by Convex Programming
, 2006
"... This paper discusses a stylized communications problem where one wishes to transmit a realvalued signal x ∈ R n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by ..."
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Cited by 50 (2 self)
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solving simple convex optimization programs, either a linear program or a secondorder cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well.
Results 11  20
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