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Solving interpolation problems via generalized eigenvalue minimization
Solving interpolation problems generalized eigenvalue minimization
2015/7/13
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...
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
2015/7/10
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...
Log-Det Heuristic for Matrix Rank Minimization with Applications to Hankel and Euclidean Distance Matrices
Log-Det Heuristic Matrix Rank Minimization Applications Hankel Euclidean Distance Matrices
2015/7/10
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...
Rank Minimization and Applications in System Theory
Rank Minimization Applications System Theory
2015/7/10
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...
Enhancing Sparsity by Reweighted l1 Minimization
Iterative reweighting Underdetermined systems of linear equations Compressive sensing Dantzig selector Sparsity
2015/7/9
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...
A Comparison of Cross-Entropy and Variance Minimization Strategies
variance minimization cross-entropy importance sampling rareevent simulation likelihood ratio degeneracy
2015/7/6
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...