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Convexification of polynomial optimization problems by means of monomial patterns. (arXiv:1901.05675v1 [math.OC])
来源于:arXiv
Convexification is a core technique in global polynomial optimization.
Currently, two different approaches compete in practice and in the literature.
First, general approaches rooted in nonlinear programming. They are
comparitively cheap from a computational point of view, but typically do not
provide good (tight) relaxations with respect to bounds for the original
problem. Second, approaches based on sum-of-squares and moment relaxations.
They are typically computationally expensive, but do provide tight relaxations.
In this paper, we embed both kinds of approaches into a unified framework of
monomial relaxations. We develop a convexification strategy that allows to
trade off the quality of the bounds against computational expenses.
Computational experiments show that a combination with a prototype
cutting-plane algorithm gives very encouraging results. 查看全文>>