holder.md

```
```@meta
CurrentModule = DataEnvelopmentAnalysis
```
# Hölder Distance Function Models
*Briec (1998)* defined technical inefficiency using Hölder norms.
## Hölder L1
In this example we compute the Hölder L1 DEA model under varible returns to scale:
```@example holder
using DataEnvelopmentAnalysis
X = [2; 4; 8; 12; 6; 14; 14; 9.412];
Y = [1; 5; 8; 9; 3; 7; 9; 2.353];
deaholder(X, Y, l = 1, rts = :VRS)
```
Estimated efficiency scores are returned with the `efficiency` function:
```@example holder
holderl1 = deaholder(X, Y, l = 1, rts = :VRS);
```
```@example holder
efficiency(holderl1)
```
The input or output that determines the projection to the frontier is returned with:
```@example holder
efficiency(holderl1, :min)
```
with inputs and outputs numbered sequentially.
## Hölder L2
!!! warning "Requieres a solver that supports SOS constraints"
The Hölder L2 model requieres a solver that supports SOS constraints, such as [Gurobi](https://github.com/jump-dev/Gurobi.jl).
Solving the model with Ipopt will return invalid results.
## Hölder LInf
In this example we compute the Hölder LInf DEA model under varible returns to scale:
```@example holder
X = [2; 4; 8; 12; 6; 14; 14; 9.412];
Y = [1; 5; 8; 9; 3; 7; 9; 2.353];
deaholder(X, Y, l = Inf, rts = :VRS)
```
### deaholder Function Documentation
```@docs
deaholder
```
```