There’s no specific arg min operator in AMPL. However, proceeding directly from the definition, you can define the arg min explicitly by a set expression like

```
{s in S: b[s] = min {i in S} b[i]}
```

This expression gives a subset of `S`

, however, containing all of the members of `S`

that achieve the minimum. To get just one member representing the arg min, you can define this to be an ordered set,

```
set b_argmin ordered := {s in S: b[s] = min {i in S} b[i]};
```

Then `first(b_argmin)`

is guaranteed to be one member of `S`

that minimizes `b[i]`

.

As an alternative, you can use AMPL’s `for`

and `if`

commands to write a script that loops over `S`

to compute the arg min explicitly:

```
param bmin;
param imin symbolic in S;
let bmin := Infinity;
for {i in S} {
if b[i] < bmin then {
let bmin := b[i];
let imin := i; } }
```

In general this is a slower alternative than defining `b_argmin`

as above. It admits a greater variety of generalizations in complex cases, however.