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I am trying to solve a single equation with multiple unknowns numerically but am kind of stuck on how to approach this. The equation I am trying to solve is ln(k1V + k2W + k3*X) = -a/T + b.

k1, k2, k3 are constants that I can provide an initial guess for but would like to optimize to minimize error. V, W, X, T are all vectors of known values a, b are constants that need to be solved for.

My initial thought was to add bounds to the values of a,b and provide guesses for k1,k2,k3 and use the least squares method to solve for a,b. I having trouble wrapping my head around how to optimize k1,k2,k3 if I am manually guessing at those values vs numerically computing everything. Any guidance or a process to find the best values of k1,k2,k3,a,b would be much appreciated.

dbhakta88
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  • Assuming that the system is overdetermined, and the lengths of (V,W,X,T) are all greater than 5. I would try to iterate the following: 1. least square optimize for (a, b) 2. reformulate the equation as k1 V + k2 W + k3 X = exp(-a/T+b) and least square optimize for (k1, k2, k3) 3.repeat the two steps until a needed precision reached – Maxim Razin Apr 19 '23 at 14:25

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