Name
Abstract | ||
|---|---|---|
The problem of finding the global minimum of a so-called Minkowski-norm dominated polynomial can be approached by the matrix method of Stetter and Moller, which reformulates it as a large eigenvalue problem. A drawback of this approach is that the matrix involved is usually very large. However, all that is needed for modern iterative eigenproblem solvers is a routine which computes the action of the matrix on a given vector. This paper focuses on improving the efficiency of computing the action of the matrix on a vector. To avoid building the large matrix one can associate the system of first-order conditions with an nD system of difference equations. One way to compute the action of the matrix efficiently is by setting up a corresponding shortest path problem and solving it. It turns out that for large n the shortest path problem has a high computational complexity, and therefore some heuristic procedures are developed for arriving cheaply at suboptimal paths with acceptable performance. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.jsc.2006.03.008 | J. Symb. Comput. |
Keywords | DocType | Volume |
global polynomial optimization,grobner basis,stetter-moller matrix method,nd-systems,large eigenvalue problems | Journal | 42 |
Issue | ISSN | Citations |
1-2 | 0747-7171 | 1 |
PageRank | References | Authors |
0.36 | 9 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ivo W. M. Bleylevens | 1 | 1 | 0.70 |
| Ralf L. M. Peeters | 2 | 62 | 22.61 |
| Bernard Hanzon | 3 | 49 | 9.54 |