Update README to follow JuMP template

README.md

@@ -3,59 +3,76 @@
 [![CI](https://github.com/samuelsonric/MathOptChordalDecomposition.jl/actions/workflows/ci.yml/badge.svg)](https://github.com/samuelsonric/MathOptChordalDecomposition.jl/actions/workflows/ci.yml)
 [![codecov](https://codecov.io/gh/samuelsonric/MathOptChordalDecomposition.jl/graph/badge.svg?token=z67ISx3vkD)](https://codecov.io/gh/samuelsonric/MathOptChordalDecomposition.jl)
 
-MathOptChordalDecomposition.jl is a [MathOptInterface.jl](https://github.com/jump-dev/MathOptInterface.jl) layer that implements chordal decomposition of
-sparse semidefinite constraints.
+MathOptChordalDecomposition.jl is a [MathOptInterface.jl](https://github.com/jump-dev/MathOptInterface.jl)
+layer that implements chordal decomposition of sparse semidefinite constraints.
 
-## Basic Usage
+## Getting help
 
-The `sdplib` directory contains four semidefinite programming problems from the [SDPLIB library](https://github.com/vsdp/SDPLIB). The function `construct_model`, defined below, reads one of the problems and constructs a [JuMP.jl](https://github.com/jump-dev/JuMP.jl) model.
+If you need help, please ask a question on the [JuMP community forum](https://jump.dev/forum).
 
-```julia-repl
-julia> using FileIO, LinearAlgebra, JuMP
+If you have a reproducible example of a bug, please [open a GitHub issue](https://github.com/samuelsonric/MathOptChordalDecomposition.jl/issues/new).
 
-julia> import MosekTools, Mosek
+## License
 
-julia> import MathOptChordalDecomposition as MOCD
+`MathOptChordalDecomposition.jl` is licensed under the
+[MIT License](https://github.com/samuelsonric/MathOptChordalDecomposition.jl/blob/master/LICENSE).
 
-julia> function construct_model(f, name::String)
-           # load data
-           data = load("./sdplib/$name.jld2");
-           F = data["F"]
-           c = data["c"]
-           m = data["m"]
-           n = data["n"]
-
-           # construct model
-           model = JuMP.Model(f)
-           set_silent(model)
-           @variable(model, x[1:m])
-           @objective(model, Min, c' * x)
-           @constraint(model, con, Symmetric(-Matrix(F[1]) + sum(Matrix(F[k + 1]) .* x[k] for k in 1:m)) in JuMP.PSDCone())
-           return model, con
-       end
-construct_model (generic function with 1 method)
-```
+## Installation
 
-Solve the problem using the [Mosek.jl](https://github.com/MOSEK/Mosek.jl) optimizer.
+Install MathOptChordalDecomposition as follows:
+```julia
+import Pkg
+Pkg.add("MathOptChordalDecomposition")
+```
 
-```julia-repl
-julia> model, con = construct_model(Mosek.Optimizer, "mcp124-1");
+## Use with JuMP
 
-julia> @time JuMP.optimize!(model)
-  6.005076 seconds (2.53 k allocations: 515.859 KiB)
+To use MathOptChordalDecomposition with JuMP, use `MathOptChordalDecomposition.Optimizer`:
 
-julia> objective_value(model)
-141.9904770422396
+```julia
+using JuMP, MathOptChordalDecomposition, SCS
+model = Model(() -> MathOptChordalDecomposition.Optimizer(SCS.Optimizer))
 ```
+Change `SCS` for any other conic solver that supports semidefinite constraints.
+
+## Basic Usage
 
-Solve the problem using [Mosek.jl](https://github.com/MOSEK/Mosek.jl) and MathOptChordalDecomposition.jl.
+The `sdplib` directory contains four semidefinite programming problems from the
+[SDPLIB library](https://github.com/vsdp/SDPLIB).
 
-```julia-repl
-julia> model, con = construct_model(() -> MOCD.Optimizer(Mosek.Optimizer), "mcp124-1");
+The function `construct_model`, defined below, reads one of the problems and
+constructs a [JuMP.jl](https://github.com/jump-dev/JuMP.jl) model.
+
+For this example, it is significantly faster to solve the problem with 
+MathOptChordalDecomposition than to use SCS by itself:
+
+```julia
+julia> using FileIO, JLD2, JuMP, LinearAlgebra, SCS
+
+julia> import MathOptChordalDecomposition as MOCD
+
+julia> function main(optimizer, name::String)
+           data = FileIO.load("./sdplib/$name.jld2");
+           F, c, m, n = data["F"], data["c"], data["m"], data["n"]    
+           model = Model(optimizer)
+           set_silent(model)
+           @variable(model, x[1:m])
+           @objective(model, Min, c' * x)
+           @constraint(
+               model,
+               con,
+               LinearAlgebra.Symmetric(-F[1] + x' * F[2:end]) in PSDCone(),
+           )
+           optimize!(model)
+           return objective_value(model)
+       end
+main (generic function with 1 method)
 
-julia> @time JuMP.optimize!(model)
-  0.041175 seconds (230.72 k allocations: 11.800 MiB)
+julia> @time main(SCS.Optimizer, "mcp124-1")
+  9.447474 seconds (154.70 k allocations: 12.313 MiB)
+141.96561765120785
 
-julia> objective_value(model)
-141.99047611570586
+julia> @time main(() -> MOCD.Optimizer(SCS.Optimizer), "mcp124-1")
+  0.245992 seconds (170.72 k allocations: 15.103 MiB, 1.85% compilation time)
+141.9887372030578
 ```