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Update README.md
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madvorak authored Sep 9, 2024
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Expand Up @@ -10,9 +10,8 @@ Instead of multiplication, we define scalar action $c \bullet \bot = \bot$ for e
$d \bullet \top = \top$ only for $d > 0$ because $0 \bullet \top = 0$.
We extend certain Farkas-like theorems to a setting where coefficients are from an extended linearly ordered field.

![AI-generated image](nonLean/AI-generated.jpg)

## Main results

* [Farkas-Bartl theorem](https://github.com/madvorak/duality/blob/f8bb1a10ee5ff811b057cdcdb50b0b668d6e8d75/Duality/FarkasBartl.lean#L216) with [explanation](FarkasBartl.pdf)
* [Strong duality for extended LP](https://github.com/madvorak/duality/blob/f8bb1a10ee5ff811b057cdcdb50b0b668d6e8d75/Duality/LinearProgramming.lean#L1021)
* [Farkas-Bartl theorem](https://github.com/madvorak/duality/blob/86026c3f8754a29f32a03864d7377767c7cfe54b/Duality/FarkasBartl.lean#L216) with [explanation](FarkasBartl.pdf)
* [Extended Farkas theorem](https://github.com/madvorak/duality/blob/86026c3f8754a29f32a03864d7377767c7cfe54b/Duality/FarkasSpecial.lean#L284)
* [Strong duality for extended linear programs](https://github.com/madvorak/duality/blob/86026c3f8754a29f32a03864d7377767c7cfe54b/Duality/LinearProgramming.lean#L1083)

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