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- Title
Lower bounds on the global minimum of a polynomial.
- Authors
Ghasemi, M.; Lasserre, J.; Marshall, M.
- Abstract
We extend the method of Ghasemi and Marshall (SIAM J. Optim. 22(2):460-473, ), to obtain a lower bound f for a multivariate polynomial $f(\mathbf{x}) \in\mathbb{R}[\mathbf {x}]$ of degree ≤2 d in n variables x=( x,..., x) on the closed ball $\{ \mathbf{x} \in\mathbb{R}^{n} : \sum x_{i}^{2d} \le M\}$, computable by geometric programming, for any real M. We compare this bound with the (global) lower bound f obtained by Ghasemi and Marshall, and also with the hierarchy of lower bounds, computable by semidefinite programming, obtained by Lasserre (SIAM J. Optim. 11(3):796-816, ). Our computations show that the bound f improves on the bound f and that the computation of f, like that of f, can be carried out quickly and easily for polynomials having of large number of variables and/or large degree, assuming a reasonable sparsity of coefficients, cases where the corresponding computation using semidefinite programming breaks down.
- Subjects
POLYNOMIALS; GEOMETRIC programming; MATHEMATICAL programming; SEMIDEFINITE programming; EVOLUTIONARY computation
- Publication
Computational Optimization & Applications, 2014, Vol 57, Issue 2, p387
- ISSN
0926-6003
- Publication type
Article
- DOI
10.1007/s10589-013-9596-x