For once, I might not be the absolute best person for this project. I'm familiar with techniques, but it would take a bit of time to on board me. So I recommend bchandra1955, he has been around for a while and I bet he will do a good job.
I actually want to be kept in the loop if you don't mind. This topic is pretty close to my expertise, but I never learned all of the nuances. Specifically for your projects, if the objective function is known and differeentiable, classic techniques like gradient descent work wonderfullly. Verifying if you have a global solution has been plaguing man ever since they developed methods for optimization. As far as I know, there are no existing methods that tell you if the solution in hand is globally optimal in a situtation where there are other "hills" or local optimals. A common technique is a Tabu Search which keeps track of solution and terminates after it reaches a solution that consistently and constantly doesn't get beaten. Simulated Annealing is another cool technique that shifts and morphs the solution space until it settles on a choice set.
I hope that helps.
If you hire someone for this project, let me know what they come up with. I can be another set of eyes and ears for you. I won't charge you, I just want to learn more.
Thanks,
SstatsC