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A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize thi...
In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification...
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
The variance minimization (VM) and cross-entropy (CE) methods are two versatile adaptive importance sampling procedures that have been successfully applied to a wide variety of difficult rare-event es...

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