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[README] clarify mode options #55

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[README] clarify mode options
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63 changes: 35 additions & 28 deletions README.md
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Expand Up @@ -74,38 +74,45 @@ List of supported model attributes:

## Options

SDPA has 3 modes that give values to all 10 parameters. By default, we put SDPA
in the `PARAMETER_DEFAULT` mode.

The three modes are as follow:

| Mode | Name |
| ------- | ----------------------------- |
| Default | `SDPA.PARAMETER_DEFAULT` |
| Fast | `SDPA.PARAMETER_UNSTABLE_BUT_FAST` |
| Slow | `SDPA.PARAMETER_STABLE_BUT_SLOW` |

The following table gives the default value for each parameter.

| Parameter name | Default | Fast | Slow |
| -------------- | ------- | ------ | ------ |
| MaxIteration | 100 | 100 | 1000 |
| EpsilonStar | 1.0e-7 | 1.0e-7 | 1.0e-7 |
| LambdaStar | 1.0e+2 | 1.0e+2 | 1.0e+4 |
| OmegaStar | 2.0 | 2.0 | 2.0 |
| LowerBound | 1.0e+5 | 1.0e+5 | 1.0e+5 |
| UpperBound | 1.0e+5 | 1.0e+5 | 1.0e+5 |
| BetaStar | 0.1 | 0.01 | 0.1 |
| BetaBar | 0.2 | 0.02 | 0.3 |
| GammaStar | 0.9 | 0.95 | 0.8 |
| EpsilonDash | 1.0e-7 | 1.0e-7 | 1.0e-7 |

Note that the parameters are set in the order they are given, so you can set it
in a mode and then modify one parameter from this mode.
SDPA has three modes that give default value to all ten parameters.

The following table gives the default values for each parameter and mode.

| Parameter | `PARAMETER_DEFAULT` | `PARAMETER_UNSTABLE_BUT_FAST` | `PARAMETER_STABLE_BUT_SLOW` |
| ------------ | ------- | ------ | ------ |
| MaxIteration | 100 | 100 | 1000 |
| EpsilonStar | 1.0e-7 | 1.0e-7 | 1.0e-7 |
| LambdaStar | 1.0e+2 | 1.0e+2 | 1.0e+4 |
| OmegaStar | 2.0 | 2.0 | 2.0 |
| LowerBound | 1.0e+5 | 1.0e+5 | 1.0e+5 |
| UpperBound | 1.0e+5 | 1.0e+5 | 1.0e+5 |
| BetaStar | 0.1 | 0.01 | 0.1 |
| BetaBar | 0.2 | 0.02 | 0.3 |
| GammaStar | 0.9 | 0.95 | 0.8 |
| EpsilonDash | 1.0e-7 | 1.0e-7 | 1.0e-7 |

By default, we put SDPA in the `SDPA.PARAMETER_DEFAULT` mode.

Change the mode using the `"Mode"` option:
```julia
using JuMP, SDPA
model = Model(SDPA.Optimizer)
set_attribute(model, "Mode", SDPA.PARAMETER_STABLE_BUT_SLOW)
```

Note that the parameters are set in the order they are given, so you can set
a mode and then modify parameters from this mode.

```julia
using JuMP, SDPA
model = Model(SDPA.Optimizer)
set_attribute(model, "Mode", SDPA.PARAMETER_STABLE_BUT_SLOW)
set_attribute(model, "MaxIteration", 100)
```

The choice of parameter mode has a large impact on the performance and stability
of SDPA, and not necessarily in the way implied by the names of the modes; for
example, `PARAMETER_UNSTABLE_BUT_FAST` can be more stable than the other modes
for some problems. You should try each mode to see how it performs on your
specific problem. See [SDPA.jl#17](https://github.com/jump-dev/SDPA.jl/issues/17)
for more details.