On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Global optimization of rational functions: a semidefinite programming approach
Mathematical Programming: Series A and B
Minimizing Polynomials via Sum of Squares over the Gradient Ideal
Mathematical Programming: Series A and B
Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares
SIAM Journal on Optimization
Global minimization of rational functions and the nearest GCDs
Journal of Global Optimization
Global Optimization of Polynomials Using the Truncated Tangency Variety and Sums of Squares
SIAM Journal on Optimization
GloptiPoly 3: moments, optimization and semidefinite programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
Global optimization of polynomials using generalized critical values and sums of squares
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Discriminants and nonnegative polynomials
Journal of Symbolic Computation
Global optimization of polynomials restricted to a smooth variety using sums of squares
Journal of Symbolic Computation
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This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as a polynomial optimization problem by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization problem. We also prove that the assumption of nonsingularity in Nie's method can be weakened to the finiteness of singularities. Some numerical examples are given in the end.