Timeline for Optimization problem where the objective function returns a function instead of a real number
Current License: CC BY-SA 4.0
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| Nov 10, 2021 at 13:53 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 10, 2021 at 1:01 | comment | added | Shaun Han | @LSpice Yes I agree the notation is confusing, but you understand it correctly. I have changed the notation from $f(x,z)$ to a function space $\mathcal{C}(x, z)$. As for $f(x_0,z) \le f(x,z)$, I mean for a given fixed interval $[c,d]$ of $z$, the curve of $f(x_0,z)$ is the lowest, i.e., $x_0$ minimizes $\int_c^d f(x, z) dz$ | |
| Nov 10, 2021 at 0:50 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 10, 2021 at 0:30 | comment | added | LSpice | I don't understand the notation $f : A \to f(x, z)$. Does it mean $f : A \times [a, b] \to \mathbb R$, where we are using $x$ as the name for an element of $A$ and $z$ as the name for an element of $[a, b]$? Also, since you allow $c = d$, it seems that your condition could be expressed more concisely as: for each $x_0 \in B$, there exists at least one $z = c = d \in [a, b]$ such that $f(x_0, z) \le f(x, z)$ for all $x \in A$, or $f(x_0, z) \ge f(x, z)$ for all $x \in A$. (And presumably you mean to pick a fixed sense of inequality, right, not allow it to differ depending on $x_0$?) | |
| Nov 10, 2021 at 0:13 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 9, 2021 at 23:51 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 9, 2021 at 23:27 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 9, 2021 at 23:21 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 9, 2021 at 23:18 | comment | added | user7868 | I think you're looking for optimal control theory, the simplest form of which is Pontryagin's maximum principle. | |
| Nov 9, 2021 at 23:04 | history | edited | Shaun Han | CC BY-SA 4.0 |
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| Nov 9, 2021 at 20:04 | review | Close votes | |||
| Nov 24, 2021 at 3:08 | |||||
| Nov 9, 2021 at 19:38 | history | asked | Shaun Han | CC BY-SA 4.0 |