Consider a linear least squares problem where the matrix involved is random. Precisely, the residual vector is
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Consider a linear least squares problem where the matrix involved is random. Precisely, the residual vector is of the form A(δ)x – b, where the m x n A matrix is affected by stochastic uncertainty. In particular, assume that
where δi, i = 1, . . . , p are i.i.d. random variables with zero mean and variance σ2i . The standard least-squares objective function ΙΙA(δ)x – bΙΙ22 is now random, since it depends on δ. We seek to determine x such that the expected value (with respect to the random variable d) ofis minimized. Is such a problem convex? If yes, to which class does it belong to (LP, LS, QP, etc.)?
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Optimization Models
ISBN: 9781107050877
1st Edition
Authors: Giuseppe C. Calafiore, Laurent El Ghaoui
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