The documentation for the trnlsp solver states that the number of equations must be at least equal to the number of variables. Does anybody know why this needs to be the case? The dtrnlsp_init function does fail if I pass m < n.
Can I bypass this by introducing dummy equations, with all values partial derivatives set to zero?
If you have an underdetermined unconstraint system, you can have an infinite set of "solutions", or no solution at all. For example, given only the equation
x^2 + 2 y^2 = -15
what do you expect the solver to give you?
Sometimes, the requested solution to an undetermined problem is a minimum norm solution.
As to providing spurious additional equations, you cannot usually expect such tricks to fool the solver into giving you a solution for a problem which we know not to have a solution.
Gradient descent methods will usually converge to a solution that is closest to the starting point. I guess that is what I was expecting. Adding dummy equations did seem to work, though the convergence rate seems very slow.