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Local and global extrema for functions of several variables
Published online by Cambridge University Press: 09 April 2009
Abstract
Let p: R2 → R be a polynomial with a local minimum at its only critical point. This must give a global minimum if the degree of p is < 5, but not necessarily if the degree is ≥ 5. It is an open question what the result is for cubics and quartics in more variables, except cubics in three variables. Other sufficient conditions for a global minimum of a general function are given.
1980 Mathematics subject classification (Amer. Math. Soc.): 26 B 99, 26 C 99.
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- Copyright © Australian Mathematical Society 1980
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