Add dualization example (#652)

* Add dualization example

* add Random

* add compat

* format

* Update docs/src/examples/general_examples/dualization.jl

Co-authored-by: Benoît Legat <[email protected]>

* update vale for dualize

* typos

* Update docs/src/examples/general_examples/dualization.jl

---------

Co-authored-by: Benoît Legat <[email protected]>
Co-authored-by: Oscar Dowson <[email protected]>

Author: 3 people

docs/Project.toml

@@ -5,6 +5,7 @@ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Dualization = "191a621a-6537-11e9-281d-650236a99e60"
 ECOS = "e2685f51-7e38-5353-a97d-a921fd2c8199"
 GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6"
 Interact = "c601a237-2ae4-5e1e-952c-7a85b0c7eef1"
@@ -23,6 +24,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 DataFrames = "1"
 Distributions = "0.25"
 Documenter = "0.27"
+Dualization = "0.5.8"
 ECOS = "1"
 GLPK = "1"
 Interact = "0.10"

docs/src/examples/general_examples/dualization.jl

@@ -0,0 +1,32 @@
+# # Dualization
+
+# Sometimes it can be much faster to solve the dual problem than the primal problem.
+# Some solvers will automatically dualize the problem when heuristics deem it beneficial,
+# and alternative DCP modeling languages like CVX will also automatically dualize the
+# problem in some cases.
+# Convex.jl does not automatically dualize any problem, but it is easy to manually do so
+# with Dualization.jl.
+# Here, we will solve a simple semidefinite program (from [issue #492](https://github.com/jump-dev/Convex.jl/issues/492)) to show how easy it is to dualize the problem,
+# and that it can potentially provide speed ups.
+
+# First we load our packages:
+using LinearAlgebra
+using Convex
+using SCS
+using Random
+using Dualization
+
+# Then we setup some test data.
+Random.seed!(2022)
+p = 50
+Σ = Symmetric(randn(p, p))
+Σ = Σ * Σ'
+
+# Now we formulate and solve our primal problem:
+d = Variable(p)
+problem = maximize(sum(d), 0 ≤ d, d ≤ 1, Σ ⪰ Diagonal(d))
+@elapsed solve!(problem, SCS.Optimizer; silent_solver = true)
+
+# To solve the dual problem instead, we simply call `dual_optimizer` on our
+# optimizer function:
+@elapsed solve!(problem, dual_optimizer(SCS.Optimizer); silent_solver = true)

docs/styles/config/vocabularies/jump-dev/accept.txt

@@ -2,6 +2,8 @@ autoregressive
 bijective
 [Bb]ugfix
 docstring
+[Dd]ualize
+[Dd]ualization
 [Ee]lementwise
 [Ee]num
 injective