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Thanks for the comments. And sorry for the inclear question. I will
re-state the problem in the following.

Suppose that d is positive integer, 1 <= d <= D. A function is defined
as follows C(d)=C1(d)+C2(d).

And for any d in 1 to D-1, we have
 C1(d) >= C1(d+1) 
 C1(d) <= C2(d+1)

Then, I have to determine that C(d) has minimum value with an optimal
value d_{op}, and to find d_{op}. I am wondering whether these
conditions are sufficient and whether I should think about or add more
conditions?

Any suggestions are greatly appreciated. Thanks and Best Regards.

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