This looks like a least squares data fitting problem with 3 domains subject to a linear constraint. a[i] is the data to be fit, b[i], c[i] and d[i] are the domains. The model is 10^(-bx-cy-dz). Seems like you could approach this a few different ways.
1. Directly fit the model and handle the constraint by using the Constrained Nonlinear Optimization.vi. This is the most straightforward to implement, but leverages little of the structure of the problem.
2. By taking the log(base 10) of a[i] the fitting problem becomes a general linear fit, although we have no way to directly handle the constraint. You could fit using this approach (General LS Linear Fit.vi), and then check for a constraint violation. This approach takes advantage of the linear nature of the problem, but does not handle the constraint well.
3. Using the same log transformation you could view the linear fitting problem as a quadratic programming problem. The advantage of this approach is that the constraint can be handled directly. The disadvantage is that the least-squares criterion is in the log domain and not the original.
4. Directly fit the model using the Nonlinear Curve Fit.vi, with the constraint transformed using a barrier approach. This is fairly straightforward to implement, but the constraint may need some fiddling to be handled as expected.
-Jim
