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New hope to correct further.md
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jajhall committed Nov 25, 2024
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20 changes: 6 additions & 14 deletions docs/src/guide/further.md
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Expand Up @@ -151,21 +151,13 @@ priority values must be distinct_.

* Add a constraint to the model so that the value of the linear objective of highest priority satsifies a bound given by the values of `abs_tolerance` and/or `rel_tolerance`.
+ If the objective was minimized to a value ``f^*\ge0``, then the constraint ensures that the this objective value is no greater than
```math
\min(f^*+`abs\_tolerance`,~f^*\times[1+`rel\_tolerance`]).
```
+ If the objective was minimized to a value ``f^*\lt0``, then the constraint ensures that the this objective value is no greater than
```math
\min(f^*+`abs\_tolerance`,~f^*\times[1-`rel\_tolerance`]).
```
``\min(f^*+abs\_tolerance,~f^*\times[1+rel\_tolerance]).``
+ If the objective was minimized to a value ``f^*<0``, then the constraint ensures that the this objective value is no greater than
``\min(f^*+abs\_tolerance,~f^*\times[1-rel\_tolerance]).``
+ If the objective was maximized to a value ``f^*\ge0``, then the constraint ensures that the this objective value is no less than
```math
\max(f^*-`abs\_tolerance`,~f^*\times[1-`rel\_tolerance`]).
```
+ If the objective was maximized to a value ``f^*\lt0``, then the constraint ensures that the this objective value is no less than
```math
\max(f^*-`abs\_tolerance`,~f^*\times[1+`rel\_tolerance`]).
```
``\max(f^*-abs\_tolerance,~f^*\times[1-rel\_tolerance]).``
+ If the objective was maximized to a value ``f^*<0``, then the constraint ensures that the this objective value is no less than
``\max(f^*-abs\_tolerance,~f^*\times[1+rel\_tolerance]).``
* Minimize/maximize with respect to the linear objective of next highest priority, and then add a corresponding objective constraint to the model, repeating until optimization with respect to the linear objective of lowest priority has taken place.

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