diff --git a/README.md b/README.md
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--- a/README.md
+++ b/README.md
@@ -1,84 +1,92 @@
-# MathOptComplements
+# MathOptComplements.jl
 
-| **Build Status** |
-|:----------------:|
-| [![Build Status][build-img]][build-url] [![Codecov branch][codecov-img]][codecov-url] |
+[![Build Status](https://github.com/jump-dev/MathOptComplements.jl/actions/workflows/ci.yml/badge.svg?branch=main)](https://github.com/jump-dev/MathOptComplements.jl/actions?query=workflow%3ACI)
+[![Codecov branch](https://codecov.io/gh/jump-dev/MathOptComplements.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/jump-dev/MathOptComplements.jl/branch/main)
 
-This package provides a set of routines to reformulate as a nonlinear program any JuMP's problem with
-[complementarity constraints](https://jump.dev/JuMP.jl/v1.29.3/moi/reference/standard_form/#MathOptInterface.Complements).
-Once reformulated, the problem can be solved using a nonlinear programming solver like [Ipopt](https://coin-or.github.io/Ipopt/).
+[MathOptComplements.jl](https://github.com/jump-dev/MathOptComplements.jl) is a
+JuMP extension for reformulating complementarity constraints.
 
-## Quick-start
+## License
+
+`MathOptComplements.jl` is licensed under the [MIT License](https://github.com/jump-dev/MathOptComplements.jl/blob/main/LICENSE.md).
+
+## Getting help
+
+If you need help, please ask a question on the [JuMP community forum](https://jump.dev/forum).
+
+If you have a reproducible example of a bug, please [open a GitHub issue](https://github.com/jump-dev/MathOptLazy.jl/issues/new).
+
+## Installation
+
+Install `MathOptComplements` using `Pkg.add`:
 
-We aim at solving the following mathematical program with complementarity constraints (MPCC):
 ```julia
-using JuMP
+import Pkg
+Pkg.add(; url = "https://github.com/jump-dev/MathOptComplements.jl")
+```
+
+## Use with JuMP
 
-model = Model()
+Use `MathOptComplements.jl` with JuMP as follows:
+```julia
+using JuMP
+import Ipopt
+import MathOptComplements
+model = Model(() -> MathOptComplements.Optimizer(Ipopt.Optimizer()))
+set_attribute(
+    model,
+    MathOptComplements.DefaultComplementarityReformulation(),
+    MathOptComplements.ScholtesRelaxation(0.0),
+)
 @variable(model, z[1:2])
 set_lower_bound(z[2], 0)
 @objective(model, Min, (z[1] - 1)^2 + z[2]^2)
-@constraint(model, [z[2] - z[1], z[2]] ∈ MOI.Complements(2))
+@constraint(model, z[2] - z[1] ⟂ z[2])
+optimize!(model)
 ```
-MathOptComplements reformulates automatically all the complementarity
-constraints using [MOI.Bridges](https://jump.dev/MathOptInterface.jl/stable/submodules/Bridges/overview/).
-Solving the problem with Ipopt and MathOptComplements just amounts to either do:
-```julia
-using Ipopt
-using MathOptComplements
 
-MathOptComplements.Bridges.add_all_bridges(model)
-set_optimizer(model, Ipopt.Optimizer)
-```
-or
+If you use Ipopt, we recommend setting the following options to improve the
+performance:
 ```julia
-using Ipopt
-using MathOptComplements
-
-set_optimizer(model, () -> MathOptComplements.Optimizer(Ipopt.Optimizer()))
-```
-before you call
-```julia
-JuMP.optimize!(model)
+set_attribute(model, "mu_strategy", "adaptive")
+set_attribute(model, "bound_push", 1e-1)
+set_attribute(model, "bound_relax_factor", 0.0)
 ```
 
-We recommend setting the following options in Ipopt to improve the performance:
-```julia
-JuMP.set_optimizer_attribute(model, "mu_strategy", "adaptive")
-JuMP.set_optimizer_attribute(model, "bound_push", 1e-1)
-JuMP.set_optimizer_attribute(model, "bound_relax_factor", 0.0)
+## Supported reformulations
 
-```
+You can change the reformulation by using the optimizer attribute
+`MathOptComplements.DefaultComplementarityReformulation`. MathOptComplements
+supports the following reformulations:
 
-## Supported reformulations
+- `MathOptComplements.ScholtesRelaxation(tau)` (**default**)
 
-You can change the reformulation by using the optimizer attribute `MathOptComplements.DefaultComplementarityReformulation`:
-```julia
-MOI.set(model, MathOptComplements.DefaultComplementarityReformulation(), MathOptComplements.ScholtesRelaxation(0.0))
-```
+  Reformulates the complementarity $0 \le a \perp b \ge 0$ as $a, b \ge 0$ and
+  $a \cdot b ≤ \tau$. For $\tau = 0$, the reformulation is exact and leads to the
+  formulation of a degenerate nonlinear program. The larger the parameter
+  $\tau \ge 0$, the better the behavior in Ipopt.
+
+- `MathOptComplements.FischerBurmeisterRelaxation(tau)`
+
+  Reformulates the complementarity $0 \le a \perp b \ge 0$ as $a, b \ge 0$ and
+  $a + b \le \sqrt{(a+b)^2 + \tau}$.
 
-> [!note]
-> The `MathOptComplements.DefaultComplementarityReformulation` attribute only works if you used
-> `set_optimizer(model, () -> MathOptComplements.Optimizer(...))`, not `MathOptComplements.Bridges.add_all_bridges(model)`.
-> That is the only difference between the two though so if you are not using setting
-> `MathOptComplements.DefaultComplementarityReformulation` because you don't change the default reformulation
-> or because you set it constraint-wise with the constraint attribute `MathOptComplements.ComplementarityReformulation`
-> then `MathOptComplements.Bridges.add_all_bridges(model)` will work.
+- `MathOptComplements.LiuFukushimaRelaxation(tau)`
 
-MathOptComplements supports the following reformulations:
-- `MathOptComplements.ScholtesRelaxation(tau)` (**default**): reformulates the complementarity `0 ≤ a ⟂ b ≥ 0` as `0 ≤ (a, b)` and `a b ≤ tau`. For `tau = 0`, the reformulation is exact and leads to the formulation of a degenerate nonlinear program. The higher the parameter `tau`, the better the behavior in Ipopt.
-- `MathOptComplements.FischerBurmeisterRelaxation(tau)`: reformulates the complementarity `0 ≤ a ⟂ b ≥ 0` as `0 ≤ (a, b)` and `a + b - sqrt((a+b)^2 + tau) ≤ 0`.
-- `MathOptComplements.LiuFukushimaRelaxation(tau)`: reformulates the complementarity `0 ≤ a ⟂ b ≥ 0` as `a b ≤ tau^2` and `(a + tau)(b + tau) ≥ tau^2`.
-- `MathOptComplements.KanzowSchwarzRelaxation(tau)`: reformulates the complementarity `0 ≤ a ⟂ b ≥ 0` as `0 ≤ (a, b)` and `ϕ(a, b) ≤ 0`, with `ϕ(a, b) = (a - tau)(b - tau)` if `a + b > 2tau`, `-0.5((a -tau)^2 + (b - tau)^2)` otherwise.
+  Reformulates the complementarity $0 \le a \perp b \ge 0$ as $a\cdot b \le \tau^2$
+  and $(a + \tau)(b + \tau) \ge \tau^2$.
 
-Most reformulations are not equivalent to the original problem, explaining why they are not activated by default.
-You can find [here](https://arxiv.org/html/2312.11022v2) a recent benchmark comparing the different reformulations on [MacMPEC](https://www.mcs.anl.gov/~leyffer/macmpec/).
+- `MathOptComplements.KanzowSchwarzRelaxation(tau)`
+
+  Reformulates the complementarity $0 \le a \perp b \ge 0$ as $a, b \ge 0$ and
+  $\phi(a, b) \le 0$, with $\phi(a, b) = (a - \tau)(b - \tau)$ if $a + b > 2\tau$,
+  $-0.5((a - \tau)^2 + (b - \tau)^2)$ otherwise.
+
+Most reformulations are not equivalent to the original problem, which is why
+they are not activated by default. [This arXiv paper](https://arxiv.org/html/2312.11022v2)
+has a recent benchmark comparing the different reformulations on [MacMPEC](https://www.mcs.anl.gov/~leyffer/macmpec/).
 
 ## Funding
 We acknowledge support from the [Fondation Mathématiques Jacques Hadamard](https://www.fondation-hadamard.fr/fr/)
-which has funded the PGMO-IROE project "A new optimization suite for large-scale market equilibrium".
-
-[build-img]: https://github.com/jump-dev/MathOptComplements.jl/actions/workflows/ci.yml/badge.svg?branch=main
-[build-url]: https://github.com/jump-dev/MathOptComplements.jl/actions?query=workflow%3ACI
-[codecov-img]: https://codecov.io/gh/jump-dev/MathOptComplements.jl/branch/main/graph/badge.svg
-[codecov-url]: https://codecov.io/gh/jump-dev/MathOptComplements.jl/branch/main
+which has funded the PGMO-IROE project "A new optimization suite for large-scale
+market equilibrium".