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Take two real differentiable convex functions, $f_1$ and $f_2$, defined on the unit interval $[0, 1]$. I want to find the global optimum of

$\min_{x \in [0,1]} a f_1(x) + b f_2(x)$

for given $a, b \in \mathbb{R}$. Is there a simple solution to this?

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    Write $f''$ as the sum between its non-negative part and its non-positive part and integrate twice...2012-10-06

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