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TitleEfficiency improvement in an systems approach to polynomial optimization
Author(s) Ivo Bleylevens, Bernard Hanzon, Ralf Peeters
TypeArticle in Journal
AbstractThe problem of finding the global minimum of a so-called Minkowski-norm dominated polynomial can be approached by the matrix method of Stetter and Möller, 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 n D 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.
KeywordsGlobal polynomial optimization, Gröbner basis, Stetter–Möller matrix method, n D systems, Large eigenvalue problem
URL http://www.sciencedirect.com/science/article/pii/S0747717106000630
JournalJournal of Symbolic Computation
Pages30 - 53
NoteEffective Methods in Algebraic Geometry (MEGA 2005)
Translation No
Refereed No