# Reformulation perspectification technique: a code example using JuMP

**URL:** <https://discourse.julialang.org/t/reformulation-perspectification-technique-a-code-example-using-jump/126729>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [March 9, 2025, 12:22pm UTC](https://discourse.julialang.org/t/reformulation-perspectification-technique-a-code-example-using-jump/126729 "2025-03-09T12:22:14Z")\
**Posts on this page:** 1\
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**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [March 16, 2025, 2:11am UTC](https://discourse.julialang.org/t/reformulation-perspectification-technique-a-code-example-using-jump/126729/3 "2025-03-16T02:11:33Z")

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This is a caveat ⚠ on the **reformulation** technique in optimization.

We (partly) encounter this problem \upsilon = \min\_{x \> 0} -x \log(x),  
which is also -\upsilon = \max\_{x \> 0} x \log(x).  
Someone may think it is a _ **convex** maximization problem_.  
Regretfully, this turns out to be an illusion **under the Max operator**.  
Indeed, the maximization problem can be reformulated as:  
\max\_x f(x), where  
f(x) = -\infty when x \le 0,  
f(x) = x \log(x) when x \> 0.  
Now we see that f is improper and **nonconvex**.

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