With a non-linear optimization problem, can insensitivity to the initial solution be interpreted as a global solution, or (high) probability of a global solution?
As I indicated in my answer to your previous similar question, you have to demonstrate insensitivity to initial solution (or starting search points) for at least a few dozens of them or more, not just a few of them. Your initial solutions (starting search points) must be random uniformly distributed points in the multidimensional solution domain. Again, there is no rigorous proof that your solution found this way is the global one. You may only state that there is a high probability that it is the global (but not 100%). The more initial solutions were used the higher that probability.
As I indicated in my answer to your previous similar question, you have to demonstrate insensitivity to initial solution (or starting search points) for at least a few dozens of them or more, not just a few of them. Your initial solutions (starting search points) must be random uniformly distributed points in the multidimensional solution domain. Again, there is no rigorous proof that your solution found this way is the global one. You may only state that there is a high probability that it is the global (but not 100%). The more initial solutions were used the higher that probability.
Accepting that generally, finding the global solution of a non-linear problem is difficult and extremely time-consuming process, a simple and straightforward answer to the question will be no!
I dont understand the notion of "insensitivity of initial solutions to a non-linear optimization problem". Unless the problem is somehow dynamic, it should not be sensitive to an initial starting point. My guess is you are talking about the sensititivity a non-linear optimization solving algorithm on a particular problem.
Then the quick answer is no.
At best you can have a probablistic idea of your optimum to be the global one as Alexander Kolker said. It will never be a formal proof, but it can be a viewed as a performance criterion of your algorithm on that specific problem.
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