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I am working on a Global Optimization problem, whose algorithm is shown in figure (1). My objective is to find two values (Gamma12 and epsilon1) for a given value of epsilon2.

I know that the upper and lower bounds of values Gamma12 and epsilon1 will be anywhere between 0.1 and -0.1.

Can anybody suggest a global optimization algorithm, i.e. the algorithm which can be able to find out the values of Gamma12 and epsilon1 at the global minimum error possible.

I tried, fminsearch, fmincon, patternsearch algorithms in matlab, the problem with those algorithms is the initial guess. I was unable to find the initial guess.

Figure 1

The_Learner
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  • The phrase "initial guess" means what it says. You can pick any value and start improving from there. `(0, 0)` is just fine. – btilly Jun 01 '18 at 17:36
  • I tried `(0, 0)` but is is not working, the value of error is very high i want the error to be in the order of `10^-5`, but I am getting `67.89` I think the program is giving local minimum. I want to find the values corresponding to global minimum @btilly – The_Learner Jun 01 '18 at 17:43
  • I'm not flagging this because I don't know the answer to the following question, but: is this more of a math question, or is this within the scope of questions allowed on Stack Overflow? – Max von Hippel Jun 01 '18 at 18:06
  • @VijayKumar Yes, hill climbing can get stuck in local minimums. Try from several random locations. Try a smaller step size. If you know what the answer is supposed to be, try with the known answer and see if you've set it up properly. – btilly Jun 01 '18 at 19:27
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    If there truly was an optimization algorithm **guaranteed** to give you the global minimum then it would be the only algorithm ever used (and the inventor would be very rich) - in general it doesn't exist. In this instance you most likely want to take a look at the [MultiStart](https://www.mathworks.com/help/gads/multistart.html) function, which will start your code at various different `x0` and return the one that gives the lowest cost. However, there is no guarantee that this will not be a local minimum. – Phil Goddard Jun 02 '18 at 15:23
  • genetic algorithm could be a good option but as Phil said its not guaranteed, – Hadi Jun 03 '18 at 18:24
  • @PhilGoddard I have an optimization algorithm guaranteed to find the global minimum, but unfortunately not in finite time. – nekomatic Jun 08 '18 at 13:23
  • @PhilGoddard , Thank you very much. At present I am using fmincon() coupled with several initial start points, hopefully the program is giving a global optima instead of stopping at a local optima. – The_Learner Jun 09 '18 at 09:43

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