I have a function in many variables, the function is concave and non-increasing in each one of the variables, is the entire function concave?
2026-04-24 00:55:10.1776992110
concavity of functions of many variables
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Consider the function $f(x,y) = xy$ on $(-\infty,0)$. Then, $f$ is concave (in fact linear) and decreasing in each variable. However, the Hessian of $f$ is indefinite.