Global optimization of polynomials using generalized critical values and sums of squares
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Representations of Positive Polynomials and Optimization on Noncompact Semialgebraic Sets
SIAM Journal on Optimization
Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities
Journal of Global Optimization
| Hi-index | 0.00 |
This paper proposes a method for finding the global infimum of a multivariate polynomial $f$ via sum of squares (SOS) relaxation over its truncated tangency variety. This variety is truncated of the set of all points $x \in \mathbb{R}^n$ where the level sets of $f$ are tangent to the sphere in $\mathbb{R}^n$ centered in the origin and with radius $\|x\|.$ It is demonstrated that: These facts imply that we can find a natural sequence of semidefinite programs whose optimal values converge monotonically, increasing to the infimum of $f.$ This opens up the possibility of solving previously intractable polynomial optimization problems.