Name
Abstract | ||
|---|---|---|
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue functions on an affine space of symmetric matrices. A linear matrix inequality (LMI) representation is given for the convex set of all feasible instances, and its boundary is studied from the perspective of algebraic geometry. This generalizes the known LMI representations of $k$-ellipses and $k$-ellipsoids. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/080722606 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
lmi representation,feasible instance,affine space,linear matrix inequality lmi,matrix cube problem,tensor product,algebraic geometry,elimination problem,semidefinite programming,symmetric matrix,maximum eigenvalue function,matrix cube,linear matrix inequality,tensor sum,semidefinite programming sdp,k-ellipse,algebraic degree.,symmetric matrices,eigenvalues,convex set | Linear algebra,Combinatorics,Matrix analysis,Matrix (mathematics),Mathematical analysis,Pure mathematics,Symmetric matrix,Eigenvalues and eigenvectors,Linear matrix inequality,Mathematics,Centrosymmetric matrix,Semidefinite programming | Journal |
Volume | Issue | ISSN |
31 | 2 | 0895-4798 |
Citations | PageRank | References |
2 | 0.42 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jiawang Nie | 1 | 537 | 38.55 |
| Bernd Sturmfels | 2 | 926 | 136.85 |