# Under what conditions the globally optimal solution and solution obtained by step-by-step optimization are the same?

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.

• Have a look at this question – David M. Jun 22 '18 at 2:26
• 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 ? – King008 Jun 22 '18 at 2:33
• 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? – Rahul Jun 22 '18 at 3:22
• – Chill2Macht Sep 2 '18 at 1:47