Solve Regularized Nonlinear Least Squares

Specific Domains Optimization (Mathematical)
1

Hi everyone :grinning:,

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.

Is it possible to solve this Regularized Nonlinear Least Squares problem with Nonlinear Least Squares solvers/interfaces such as

Or is it mandatory to use more general optimization (Optimization.jl) to solve it?

Thanks!
fdekerm

2

It’s possible, there are methods to do this, but I don’t know of any software that does it right now…

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