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More specifically, I have a problem where it is hard to find the optimal solution w.r.t all the parameters together, so I solve it w.r.t one parameter at a time. In each step, I either use the optimal value of other parameters obtained from the previous step or just keep them as variables to be optimized later. I can not prove the convexity / concavity of the problem but can show the objective function to be monotone w.r.t all the parameters. Thanks in Advance.

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  • $\begingroup$ Have a look at this question $\endgroup$ – David M. Jun 22 '18 at 2:26
  • $\begingroup$ Thanks David. It is exactly what I am already doing, but the answer doesn't specify when will the solution be equal to the global one? Is there any theorem / result that I can refer to ? $\endgroup$ – King008 Jun 22 '18 at 2:33
  • $\begingroup$ Are you sure you're doing that and not coordinate descent? Also, if the objective is monotone then it can't have an optimum except at the boundary, can it? $\endgroup$ – Rahul Jun 22 '18 at 3:22
  • $\begingroup$ See also math.stackexchange.com/questions/453831/… $\endgroup$ – Chill2Macht Sep 2 '18 at 1:47

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