Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a continuous, differentiable function. Is there a known algorithm that fits $f$ with $g$, which is an order-$n$ polynomial that is convex, in the least square sense?
Approximating a function with a convex function
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linear-algebra
optimization
convex-optimization
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1What do you mean by least square in this context, i.e. what objective are you minimizing? – 2012-12-31
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0I would like to minimize the $l_2$-norm of $(f-g)$ – 2012-12-31
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1Given the examples below, perhaps you want to restrict the function to a bounded interval? – 2012-12-31
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0Yes. It would be more interesting if the supports of $f$ and $g$ are bounded intervals. – 2012-12-31