Abstract
This paper addresses the problem of finding tight affine lower bound functions for multivariate polynomials. Such underestimating functions are needed if global optimization problems involving polynomials are solved with a branch and bound method. These bound functions are constructed by using the expansion of the given polynomial into Bernstein polynomials. In contrast to our previous method which requires in the general case the solution of a linear programming problem, we propose here a method which requires only the solution of a system of linear equations together with a sequence of back substitutions and the computation of slopes. An error bound exhibiting quadratic convergence in the univariate case and some numerical examples are presented.
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Garloff, J., Smith, A.P. (2004). An Improved Method for the Computation of Affine Lower Bound Functions for Polynomials. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_8
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DOI: https://doi.org/10.1007/978-1-4613-0251-3_8
Publisher Name: Springer, Boston, MA
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