# Finding the minimizer region of a function

**URL:** <https://discourse.julialang.org/t/finding-the-minimizer-region-of-a-function/103819>\
**Category:** Numerics\
**Tags:** optimization\
**Created:** [September 13, 2023, 4:31pm UTC](https://discourse.julialang.org/t/finding-the-minimizer-region-of-a-function/103819 "2023-09-13T16:31:55Z")\
**Posts on this page:** 1\
**Showing post:** 13

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**Author:** ![yosuga](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yosuga/32/52638_2.png) [@yosuga](https://discourse.julialang.org/u/yosuga)\
**Post date:** [September 17, 2023, 7:01am UTC](https://discourse.julialang.org/t/finding-the-minimizer-region-of-a-function/103819/13 "2023-09-17T07:01:51Z")

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I understand the theoretical expectations, but I’m not sure whether a numerical calculation works or not. Since the integrand of the Ronkin function has a logarithmic singularity on Amoeba, one may get an incorrect result about optimization. Actually, [I have failed to evaluate Laplacian (of a-space) for a different model](https://discourse.julialang.org/t/laplacian-for-a-minimized-function/103836).

But I tried to calculate Laplacian (of x-space) for the present cases, the results look good. So if Optim.jl always gives a correct minimizer, namely a point in the vacuole, one would distinguish the difference. Thank you.

 ![laplacian-a=2](https://global.discourse-cdn.com/julialang/original/3X/7/c/7c710f1c8c8749199ec5e5c8ad599cc9e221b4ce.png)  
 ![laplacian-a=2.05](https://global.discourse-cdn.com/julialang/original/3X/8/0/802149bc6067e28e57c4b9b512cb974f3e9f7ae5.png)

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