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If an exercise says:

Let $X=\{x:x\ge0\}$. Find the dual function of the minimization problem $c^tx$ s.t. $Ax=b,x\ge0$.

And If I write:

The dual function is given by $\max\theta$, where $\theta =\inf\{f(x)+u^tg(x):x\in X\}$, where $f(x)=c^tx$ and $g(x)=Ax-b$, then is my answer

incorrect?

or correct?

or how is it?

As you can see, the task is to find, but it does not says find explicitly nor find implicity.

And I did find it (implicitly)

user441848
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  • Well, if you can solve the exercise in one line then generally, you did not do enough, I assume. Can $\theta$ be computed concretly ? If so, I guess you are intended to do so. – Suzet Jul 03 '18 at 01:43
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    In which book did you find this excercise? – Frank Moses Jul 03 '18 at 01:47
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    If I asked students to find the solution set of the equation $x^2-2x+7=0$, I would not give any credit for “The solution set is ${x\in\mathbb C : x^2-2x+7=0}$,” and I would not feel too bad about it, even though the statement is true. – Steve Kass Jul 03 '18 at 01:48
  • @SteveKass but the answer it's actually correct. :) you didn't write find explicitly – user441848 Jul 03 '18 at 01:53
  • @user441848 Define "explicitly." – Clement C. Jul 03 '18 at 01:55
  • @ClementC. Taking the example Steve provided, the explicit solution would be something like $x=4,-1$ (no real answer just an example) – user441848 Jul 03 '18 at 01:58
  • So... You know "explicit" when you see it? The appropriate definition is context-dependent, as is that of "closed form." Want to go down that rabbit hole? – Clement C. Jul 03 '18 at 02:01
  • @Suzet or maybe I am not intented to do so, it does not says find explicitly – user441848 Jul 03 '18 at 02:05
  • @FrankMoses Nonlinear Programming by Bazaraa. Why? – user441848 Jul 03 '18 at 02:06
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    @user441848 In the question you posted here https://math.stackexchange.com/questions/2759901/how-to-find-the-sum-1-frac12-frac14-frac15-frac17-frac1 "how to find the sum [...]", you did not write "explicitly", but I am sure you would not have been satisfied with the answer "Well, this sum equals $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots$". – Suzet Jul 03 '18 at 02:09
  • @Suzet haha no of course not, I'd be upset, but that clearly does not mean that your answer "Well, this sum equals $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots"$ is incorrect. – user441848 Jul 03 '18 at 02:12

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