# Solve Regularized Nonlinear Least Squares
**URL:** https://discourse.julialang.org/t/solve-regularized-nonlinear-least-squares/129608
**Category:** Optimization (Mathematical)
**Tags:** optimization
**Created:** [June 3, 2025, 5:34pm UTC](https://discourse.julialang.org/t/solve-regularized-nonlinear-least-squares/129608 "2025-06-03T17:34:56Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@fdekerme](https://discourse.julialang.org/u/fdekerme)
#### Post date: [June 3, 2025, 5:34pm UTC](https://discourse.julialang.org/t/solve-regularized-nonlinear-least-squares/129608/1 "2025-06-03T17:34:56Z")
Hi everyone 😀,
I want to solve a large Regularized Nonlinear Least Squares problem
min \text{Cost} \left(T^{1}, T^{2}\right) = \|r\|^2 + R(T^{1}, T^{2})
where r log-sum-exponential terms:
r^{i}(T^{1}, T^{2}) = \log \left(\sum\_K K \exp \left(-T^{1} v\_K^{1} - T^{2} v\_K^{2} \right) \right) - \log \left(Y^{i}\right)
and R(T^{1}, T^{2}) a (user defined) regularization, such as a [Huber loss](https://en.wikipedia.org/wiki/Huber_loss).
Is it possible to solve this Regularized Nonlinear Least Squares problem with Nonlinear Least Squares solvers/interfaces such as
- [NonlinearSolve.jl](https://docs.sciml.ai/NonlinearSolve/stable/solvers/nonlinear_least_squares_solvers/) from [SciML](https://sciml.ai/)
- CaNNOLeS.jl or JSOSolvers.jl from [JuliaSmoothOptimizers](https://github.com/JuliaSmoothOptimizers)
- [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl)
- [NLLSsolver.jl](https://github.com/ojwoodford/NLLSsolver.jl)
- Enlsip.jl
- others ?
Or is it mandatory to use more general optimization (Optimization.jl) to solve it?
Thanks!
fdekerm
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [June 3, 2025, 10:01pm UTC](https://discourse.julialang.org/t/solve-regularized-nonlinear-least-squares/129608/2 "2025-06-03T22:01:20Z")
It’s possible, there are methods to do this, but I don’t know of any software that does it right now…