State space realization of 2-D finite-dimensional behaviours
SIAM Journal on Control and Optimization
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
SIAM Journal on Scientific Computing
Communications of the ACM
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Global Minimization of a Multivariate Polynomial using Matrix Methods
Journal of Global Optimization
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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.