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I need to find the minimum/maximum of a nonlinear function but the constraints in the optimization problem make it tougher to solve (not a convex problem). I don't have a good global optimization algorithm available, so instead, I use a local optimization algorithm with gradients and check the solution by giving the algorithm several different starting values. If all of these starting values lead to the same solution, am I actually performing global optimization?

I'm interested in knowing whether this kind of an approach (using local algorithm, checking solution with multiple starting values) is reasonable and I could claim that I have (likely) found the global optimum?

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  • $\begingroup$ Hi, it is a reasonable approach as long as you can sample the starting points from a set that contains the feasible one. In general you'll get no convergence results (well maybe in probability). Search the net for multi-start methods and you'll find plenty of methods. $\endgroup$ – AndreaCassioli Jan 26 '15 at 16:09

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