example9 #138
example9 #138
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@odow, could you please check the model and tell me how I should write the model? |
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| # Model with doul variable | ||
| # ```math | ||
| # \min 40000x + 8760*(10y_1-\lambda * y_1),\\ |
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Where does the 8760 come from? What is \lambda?
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lambda is the dual variable of one of the constraints in the second-level problem.
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8760 is the number of hours in the year.
that is part of the formulation in the paper. as @odow said we should add a tiny bit of context. Explaining physical meaning of variables and constraints....
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| # # Foundations of Bilevel Programming: Example 9 | |||
| # This example is from the book Investment in Electricity Generation and Transmission. [url](https://www.springer.com/gp/book/9783319294995) | |||
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Since this example is more realistic, it needs a description of the physical problem. What the variables represent, etc.
Some (not all. I can do better) of the JuMP tutorials do this:
https://jump.dev/JuMP.jl/stable/tutorials/Nonlinear%20programs/space_shuttle_reentry_trajectory/
https://jump.dev/JuMP.jl/stable/tutorials/Mixed-integer%20linear%20programs/sudoku/
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Yes, we need a bit of story telling, nothing complex. something like:
In this example we consider a power system with two existing generators and one being planned.
Their costs are... and existing generators have... available capacity.
The problem is to optimize the size of the new generators given that....
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| # Model with doul variable | ||
| # ```math | ||
| # \min 40000x + 8760*(10y_1-\lambda * y_1),\\ |
There was a problem hiding this comment.
8760 is the number of hours in the year.
that is part of the formulation in the paper. as @odow said we should add a tiny bit of context. Explaining physical meaning of variables and constraints....
docs/src/examples/IEGT_example1.jl
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| # y_2 \leq 150,\\ | ||
| # y_3 \leq 100,\\ | ||
| # y[i] \geq 0, \forall i \in I\\ | ||
| # ``` |
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we should go straight to model with dual
docs/src/examples/IEGT_example1.jl
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| # ```math | ||
| # \min 10y_1 + 12y_2 + 15y_3,\\ | ||
| # \notag s.t.\\ | ||
| # y_1 + y_2 + y_3 = 200,\\ |
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| # y_1 + y_2 + y_3 = 200,\\ | |
| # y_1 + y_2 + y_3 = 200, \quad [\lambda]\\ |
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