Name
Abstract | ||
|---|---|---|
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically, this degree counts the critical points attained by a linear functional on a fixed rank locus in a linear space of symmetric matrices. We determine this degree using methods from complex algebraic geometry, such as projective duality, determinantal varieties, and their Chern classes. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10107-008-0253-6 | Math. Program. |
Keywords | Field | DocType |
genericity,complex algebraic geometry,chern class. 1,multidegree,semidefinite programming,minimal polynomial,critical point,chern class,fixed rank locus,generic semidefinite program,algebraic degree,optimal solution,. semidefinite programming,euler-poincare characteristic,determi- nantal variety,determinantal variety,algebraic number,dual variety,linear space,algebraic geometry,symmetric matrices | Discrete mathematics,Dimension of an algebraic variety,Mathematical optimization,Function field of an algebraic variety,Differential algebraic geometry,Algebraic surface,Algebraic cycle,Algebraic extension,Real algebraic geometry,Mathematics,Bézout's theorem | Journal |
Volume | Issue | ISSN |
122 | 2 | 1436-4646 |
Citations | PageRank | References |
28 | 2.75 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jiawang Nie | 1 | 537 | 38.55 |
| Kristian Ranestad | 2 | 62 | 8.18 |
| Bernd Sturmfels | 3 | 926 | 136.85 |