lsqnonlin is a numerical optimization tool. It iterations fro mthe start point to a solution. And the solution you get is dependent on where you start.
The analogy I use is to imagine a blind person, set down on the face of the earth, and tasked with finding the point of lowest elevation. All he can do to determine where to walk next is a cane. Please, give him some scuba gear. But it matters a lot if you put him down in different locations. Near the dead sea, for example, would be a bad start point, since he will get stuck in an unfortunate spot. When the person can no longer find a route down from where they are standing, they stop, and annnounce a solution.
There is a concept known as the basin of attraction. So if you picked many start points, all of which were close to the same spot, then they will all end up at essentially the same final point. The basin of attraction for any solution is the set of start points that will converge to that solution.
The point is, you get ONE answer, and one only. If you want multiple solutions, then start at multiple various start points, and hope that one of them is near the lowest point. Intelligently chosen start points are likely better than not.
