"Augabog" wrote...
....
I'm using SOLVER to change three variables in order to get a
minimum sum squared error. I've noticed that if I change the
initial values for the 3 variables before running solver,
that the solver will return different values! There should
only be one value for each associated with a minimum sum of
squared error, and I have placed non constraints on what
Excel can change the three variables in order to reach that
minimum value for the target cell . . . Therefore, what the
values for those three cells are prior to running the
solver shouldn't matter, . . .

Well, you're dead wrong.

First off, Solver, like any other iterative numerical optimization
software, only iterates until the change between a specified number of
iterations is less than a specified threshold. If the initial values
lead to a plateau or local minimum, that's what Solver is going to
give as its result, even if it's not a GLOBAL minimum. There are
settings in Solver's Options dialog which YOU can change to increase
the odds of Solver winding up with a global minimum.

There's a lot of literature on the pitfalls of numerical optimization.
You might want to consider buying a textbook on the subject.