Algorithm for multidimensional constrained root finding

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A user is seeking a Fortran algorithm for multidimensional constrained root finding to determine steady-state solutions for a dynamic model with approximately 60 state variables and coupled differential equations. They are currently using a modified Newton-Raphson method but face issues with convergence and lack of support for bounds. The user has identified a BFGS implementation that accommodates constraints but is unsure of its suitability for root finding. They are open to suggestions for better algorithms and emphasize the importance of testing implementations to determine effectiveness. The discussion highlights the challenges of finding appropriate multidimensional algorithms that support constraints in root finding.
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Hi all,

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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It is probably best to implement it and test it. Should be faster than searching for other algorithms without knowing the outcome.
 

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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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