Timeline for Constrained linear optimization problem on $C^1$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2023 at 10:57 | comment | added | Hyperbolic PDE friend | I see, thanks a lot! | |
| Mar 9, 2023 at 10:20 | comment | added | cs89 | The supremum with $v \in C^1$ or $v \in C^\infty$ is the same. You only need to change the construction of the sequence $v_n$. With my notations, you want to construct $v_n \in C^\infty([0,1])$ with $v_n(x) = 1$ for $x \in [1/n,1]$, $v_n(0) = \sigma$, and $\sigma \leq v_n(x) \leq 1$ on $[0,1/n]$. Making a $C^\infty$ junction at $x =1/n$ is rather standard. You can choose $v_n(x) = 1+(\sigma-1) \exp(1-1/s^2)$ where $s = n(x-1/n)$. | |
| Mar 9, 2023 at 9:12 | comment | added | Hyperbolic PDE friend | and $o \in C^\infty(\mathbb{R})$ for that matter. | |
| Mar 9, 2023 at 8:54 | comment | added | Hyperbolic PDE friend | This is a great answer, thank you! Do you have any idea what happens when we additionaly demand $u \in W^{\infty, \infty}([a, b])$? | |
| Mar 9, 2023 at 8:54 | vote | accept | Hyperbolic PDE friend | ||
| Mar 9, 2023 at 8:46 | comment | added | cs89 | The same argument also works for the maximization version. I edited my answer. | |
| Mar 9, 2023 at 8:45 | history | edited | cs89 | CC BY-SA 4.0 |
Changed minimization problem to maximization as asked by @Meowdog
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| Mar 9, 2023 at 8:18 | comment | added | Hyperbolic PDE friend | This is a very good answer, thank you! But I made a mistake myself... I wanted the problem to be a maximum problem and I wrote minimum. Still, I hope that I can maybe rewrite your argument... I would still be happy if you could provide some insight | |
| Mar 9, 2023 at 0:19 | history | answered | cs89 | CC BY-SA 4.0 |