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I'm looking for an algorithm for multidimensional constrained root finding, implemented in Fortran. It's intended for finding a steady-state solution for a dynamic model. I have n state variables and n coupled differential equations (n~=60), and I need to find the value for the state variables at which the rate of change is zero.

Currently I'm working with an adapted version of Newton-Raphson taken from Numerical Recipes, but this algorithm doesn't support bounds and the solver has a tendency to converge on impossible values. Actually, it seems that not many multidimensional algorithms support bounds. I found an implementation of BFGS (http://hod.greeley.org/papers/Unsorted/lbfgsb.pdf) that supports constraints, but I'm not sure if this suitable for my purpose. From what I understand, not every minimization algorithm is suitable for root finding.

Can anyone tell me if the BGFS algorithm is suitable for root finding, or suggest a better algorithm?

Many thanks in advance!

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# Algorithm for multidimensional constrained root finding

Can you offer guidance or do you also need help?

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