# Parameter estimation with norm vs. norm-squared loss

**URL:** <https://discourse.julialang.org/t/parameter-estimation-with-norm-vs-norm-squared-loss/90394>\
**Category:** Modelling & Simulations\
**Tags:** sciml\
**Created:** [November 17, 2022, 10:06am UTC](https://discourse.julialang.org/t/parameter-estimation-with-norm-vs-norm-squared-loss/90394 "2022-11-17T10:06:17Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![fhchl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fhchl/32/35902_2.png) [@fhchl](https://discourse.julialang.org/u/fhchl)\
**Post date:** [November 17, 2022, 10:06am UTC](https://discourse.julialang.org/t/parameter-estimation-with-norm-vs-norm-squared-loss/90394/1 "2022-11-17T10:06:17Z")

</div>

In the SciML book, parameter estimation problems are defined with a loss function that uses the norm of the residual, not the norm-squared as typical in least-squares formulations (see [here](https://book.sciml.ai/notes/10-Basic_Parameter_Estimation-Reverse-Mode_AD-and_Inverse_Problems/)). Is this a typo or is there more behind it? As the square is convex, I presume the minima do not change, but I would expect a different behavior of gradient descend in both cases.