I am performing a least-squares, non-linear constrained optimization problem with the following structure:
Called the summands (whose sum of squares I want to minimize) DQ_i. One parameter, theta, affects all the DQ_i. For a given theta, the constraints uniquely determine the rest of the parameters. Further, the constraints are segmented so I could solve for different chunks of the parameters separately (given theta). However, any solution would be numeric.
So I could structure the problem in two ways:
1) Frame it as a nested optimization problem. Pick a theta, solve the smaller problems in chunks, calculate the objective function, and repeat.
2) Put all the parameters together and solve it as one big, constrained problem.
Which approach is more advisable? 2) seems cleaner from a MATLAB coding perspective since if the constraint-solving fails even once, it will derail the whole problem. But 1) seems potentially faster as I never have too many variables to solve for at once.